LMFDB - Embedded newform 2664.1.m.a.739.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2664,1,Mod(739,2664)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2664, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2664.739");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2664 = 2^{3} \cdot 3^{2} \cdot 37$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2664.m (of order $2$ , degree $1$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.32950919365$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x - 1$ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 296)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.87616.1

Embedding invariants

Embedding label			739.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2664.739

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} -0.618034 q^{5} -1.00000 q^{8} +0.618034 q^{10} -0.618034 q^{11} -1.61803 q^{13} +1.00000 q^{16} -0.618034 q^{20} +0.618034 q^{22} +1.61803 q^{23} -0.618034 q^{25} +1.61803 q^{26} +1.61803 q^{29} +0.618034 q^{31} -1.00000 q^{32} +1.00000 q^{37} +0.618034 q^{40} +1.61803 q^{41} -0.618034 q^{44} -1.61803 q^{46} +1.00000 q^{49} +0.618034 q^{50} -1.61803 q^{52} +0.381966 q^{55} -1.61803 q^{58} +0.618034 q^{61} -0.618034 q^{62} +1.00000 q^{64} +1.00000 q^{65} +0.618034 q^{67} +0.618034 q^{73} -1.00000 q^{74} -1.61803 q^{79} -0.618034 q^{80} -1.61803 q^{82} -2.00000 q^{83} +0.618034 q^{88} +1.61803 q^{92} -1.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{2} + 2 q^{4} + q^{5} - 2 q^{8} - q^{10} + q^{11} - q^{13} + 2 q^{16} + q^{20} - q^{22} + q^{23} + q^{25} + q^{26} + q^{29} - q^{31} - 2 q^{32} + 2 q^{37} - q^{40} + q^{41} + q^{44}+ \cdots - 2 q^{98}+O(q^{100})$ 2 * q - 2 * q^2 + 2 * q^4 + q^5 - 2 * q^8 - q^10 + q^11 - q^13 + 2 * q^16 + q^20 - q^22 + q^23 + q^25 + q^26 + q^29 - q^31 - 2 * q^32 + 2 * q^37 - q^40 + q^41 + q^44 - q^46 + 2 * q^49 - q^50 - q^52 + 3 * q^55 - q^58 - q^61 + q^62 + 2 * q^64 + 2 * q^65 - q^67 - q^73 - 2 * q^74 - q^79 + q^80 - q^82 - 4 * q^83 - q^88 + q^92 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2664\mathbb{Z}\right)^\times$ .

$n$	$1297$	$1333$	$1999$	$2369$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	−1.00000	−1.00000
$2$	−1.00000	−1.00000
$3$	0	0
$3$	0	0
$4$	1.00000	1.00000
$5$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−1.00000	−1.00000
$9$	0	0
$10$	0.618034	0.618034
$11$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$11$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$12$	0	0
$13$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$13$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−0.618034	−0.618034
$21$	0	0
$22$	0.618034	0.618034
$23$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$23$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$24$	0	0
$25$	−0.618034	−0.618034
$26$	1.61803	1.61803
$27$	0	0
$28$	0	0
$29$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$29$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$30$	0	0
$31$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$31$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$32$	−1.00000	−1.00000
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.00000	1.00000
$37$	1.00000	1.00000
$38$	0	0
$39$	0	0
$40$	0.618034	0.618034
$41$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$41$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−0.618034	−0.618034
$45$	0	0
$46$	−1.61803	−1.61803
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	1.00000	1.00000
$50$	0.618034	0.618034
$51$	0	0
$52$	−1.61803	−1.61803
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0.381966	0.381966
$56$	0	0
$57$	0	0
$58$	−1.61803	−1.61803
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$61$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$62$	−0.618034	−0.618034
$63$	0	0
$64$	1.00000	1.00000
$65$	1.00000	1.00000
$66$	0	0
$67$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$67$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$73$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$74$	−1.00000	−1.00000
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$80$	−0.618034	−0.618034
$81$	0	0
$82$	−1.61803	−1.61803
$83$	−2.00000	−2.00000	−1.00000			$\pi$
$83$	−2.00000	−2.00000	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0.618034	0.618034
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	1.61803	1.61803
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.00000	−1.00000
$99$	0	0
$100$	−0.618034	−0.618034
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$103$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$104$	1.61803	1.61803
$105$	0	0
$106$	0	0
$107$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$107$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$108$	0	0
$109$	2.00000	2.00000	1.00000			$0$
$109$	2.00000	2.00000	1.00000			$0$
$110$	−0.381966	−0.381966
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	−1.00000	−1.00000
$116$	1.61803	1.61803
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−0.618034	−0.618034
$122$	−0.618034	−0.618034
$123$	0	0
$124$	0.618034	0.618034
$125$	1.00000	1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	0	0
$130$	−1.00000	−1.00000
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−0.618034	−0.618034
$135$	0	0
$136$	0	0
$137$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$137$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$138$	0	0
$139$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$139$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	1.00000	1.00000
$144$	0	0
$145$	−1.00000	−1.00000
$146$	−0.618034	−0.618034
$147$	0	0
$148$	1.00000	1.00000
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−0.381966	−0.381966
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	1.61803	1.61803
$159$	0	0
$160$	0.618034	0.618034
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	1.61803	1.61803
$165$	0	0
$166$	2.00000	2.00000
$167$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$167$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$168$	0	0
$169$	1.61803	1.61803
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−0.618034	−0.618034
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	−1.61803	−1.61803
$185$	−0.618034	−0.618034
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$191$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	1.00000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	2.00000	2.00000	1.00000			$0$
$199$	2.00000	2.00000	1.00000			$0$
$200$	0.618034	0.618034
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−1.00000	−1.00000
$206$	−0.618034	−0.618034
$207$	0	0
$208$	−1.61803	−1.61803
$209$	0	0
$210$	0	0
$211$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$211$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$212$	0	0
$213$	0	0
$214$	−1.61803	−1.61803
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−2.00000	−2.00000
$219$	0	0
$220$	0.381966	0.381966
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	1.00000	1.00000
$231$	0	0
$232$	−1.61803	−1.61803
$233$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$233$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$239$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0.618034	0.618034
$243$	0	0
$244$	0.618034	0.618034
$245$	−0.618034	−0.618034
$246$	0	0
$247$	0	0
$248$	−0.618034	−0.618034
$249$	0	0
$250$	−1.00000	−1.00000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	−1.00000	−1.00000
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	1.00000	1.00000
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0.618034	0.618034
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0.618034	0.618034
$275$	0.381966	0.381966
$276$	0	0
$277$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$277$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$278$	1.61803	1.61803
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	−1.00000	−1.00000
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	1.00000	1.00000
$291$	0	0
$292$	0.618034	0.618034
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	−1.00000	−1.00000
$297$	0	0
$298$	0	0
$299$	−2.61803	−2.61803
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	−0.381966	−0.381966
$306$	0	0
$307$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$307$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$308$	0	0
$309$	0	0
$310$	0.381966	0.381966
$311$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$311$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	−1.61803	−1.61803
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	−1.00000	−1.00000
$320$	−0.618034	−0.618034
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	1.00000	1.00000
$326$	0	0
$327$	0	0
$328$	−1.61803	−1.61803
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	−2.00000	−2.00000
$333$	0	0
$334$	0.618034	0.618034
$335$	−0.381966	−0.381966
$336$	0	0
$337$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$337$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$338$	−1.61803	−1.61803
$339$	0	0
$340$	0	0
$341$	−0.381966	−0.381966
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0.618034	0.618034
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−0.381966	−0.381966
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	1.61803	1.61803
$369$	0	0
$370$	0.618034	0.618034
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−2.61803	−2.61803
$378$	0	0
$379$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$379$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$380$	0	0
$381$	0	0
$382$	0.618034	0.618034
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$389$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−1.00000
$393$	0	0
$394$	0	0
$395$	1.00000	1.00000
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	−2.00000	−2.00000
$399$	0	0
$400$	−0.618034	−0.618034
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	−1.00000	−1.00000
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−0.618034	−0.618034
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	1.00000	1.00000
$411$	0	0
$412$	0.618034	0.618034
$413$	0	0
$414$	0	0
$415$	1.23607	1.23607
$416$	1.61803	1.61803
$417$	0	0
$418$	0	0
$419$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$419$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$420$	0	0
$421$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$422$	−0.618034	−0.618034
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	1.61803	1.61803
$429$	0	0
$430$	0	0
$431$	−2.00000	−2.00000	−1.00000			$\pi$
$431$	−2.00000	−2.00000	−1.00000			$\pi$
$432$	0	0
$433$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$433$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$434$	0	0
$435$	0	0
$436$	2.00000	2.00000
$437$	0	0
$438$	0	0
$439$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$439$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$440$	−0.381966	−0.381966
$441$	0	0
$442$	0	0
$443$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$443$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	−1.00000	−1.00000
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	−1.00000	−1.00000
$461$	−2.00000	−2.00000	−1.00000			$\pi$
$461$	−2.00000	−2.00000	−1.00000			$\pi$
$462$	0	0
$463$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$463$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$464$	1.61803	1.61803
$465$	0	0
$466$	−1.61803	−1.61803
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0.618034	0.618034
$479$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$479$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$480$	0	0
$481$	−1.61803	−1.61803
$482$	0	0
$483$	0	0
$484$	−0.618034	−0.618034
$485$	0	0
$486$	0	0
$487$	2.00000	2.00000	1.00000			$0$
$487$	2.00000	2.00000	1.00000			$0$
$488$	−0.618034	−0.618034
$489$	0	0
$490$	0.618034	0.618034
$491$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$491$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0.618034	0.618034
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	1.00000	1.00000
$501$	0	0
$502$	0	0
$503$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$503$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$504$	0	0
$505$	0	0
$506$	1.00000	1.00000
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−1.00000
$513$	0	0
$514$	0	0
$515$	−0.381966	−0.381966
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−1.00000	−1.00000
$521$	−2.00000	−2.00000	−1.00000			$\pi$
$521$	−2.00000	−2.00000	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.61803	1.61803
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−2.61803	−2.61803
$534$	0	0
$535$	−1.00000	−1.00000
$536$	−0.618034	−0.618034
$537$	0	0
$538$	0	0
$539$	−0.618034	−0.618034
$540$	0	0
$541$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$541$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−1.23607	−1.23607
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	−0.618034	−0.618034
$549$	0	0
$550$	−0.381966	−0.381966
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−0.618034	−0.618034
$555$	0	0
$556$	−1.61803	−1.61803
$557$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$557$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$572$	1.00000	1.00000
$573$	0	0
$574$	0	0
$575$	−1.00000	−1.00000
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.00000	−1.00000
$579$	0	0
$580$	−1.00000	−1.00000
$581$	0	0
$582$	0	0
$583$	0	0
$584$	−0.618034	−0.618034
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	1.00000	1.00000
$593$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$593$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	2.61803	2.61803
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$601$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0.381966	0.381966
$606$	0	0
$607$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$607$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$608$	0	0
$609$	0	0
$610$	0.381966	0.381966
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	1.61803	1.61803
$615$	0	0
$616$	0	0
$617$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$617$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$618$	0	0
$619$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$619$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$620$	−0.381966	−0.381966
$621$	0	0
$622$	−1.61803	−1.61803
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$632$	1.61803	1.61803
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−1.61803	−1.61803
$638$	1.00000	1.00000
$639$	0	0
$640$	0.618034	0.618034
$641$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$641$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$647$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$648$	0	0
$649$	0	0
$650$	−1.00000	−1.00000
$651$	0	0
$652$	0	0
$653$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$653$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$654$	0	0
$655$	0	0
$656$	1.61803	1.61803
$657$	0	0
$658$	0	0
$659$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$659$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$660$	0	0
$661$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$662$	0	0
$663$	0	0
$664$	2.00000	2.00000
$665$	0	0
$666$	0	0
$667$	2.61803	2.61803
$668$	−0.618034	−0.618034
$669$	0	0
$670$	0.381966	0.381966
$671$	−0.381966	−0.381966
$672$	0	0
$673$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$673$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$674$	−0.618034	−0.618034
$675$	0	0
$676$	1.61803	1.61803
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0.381966	0.381966
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0.381966	0.381966
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	2.00000	2.00000	1.00000			$0$
$691$	2.00000	2.00000	1.00000			$0$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	1.00000	1.00000
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$701$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$702$	0	0
$703$	0	0
$704$	−0.618034	−0.618034
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$709$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	1.00000	1.00000
$714$	0	0
$715$	−0.618034	−0.618034
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−1.00000	−1.00000
$723$	0	0
$724$	0	0
$725$	−1.00000	−1.00000
$726$	0	0
$727$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$727$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$728$	0	0
$729$	0	0
$730$	0.381966	0.381966
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	−1.61803	−1.61803
$737$	−0.381966	−0.381966
$738$	0	0
$739$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$740$	−0.618034	−0.618034
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	2.61803	2.61803
$755$	0	0
$756$	0	0
$757$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$757$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$758$	1.61803	1.61803
$759$	0	0
$760$	0	0
$761$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$761$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$762$	0	0
$763$	0	0
$764$	−0.618034	−0.618034
$765$	0	0
$766$	2.00000	2.00000
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	−0.381966	−0.381966
$776$	0	0
$777$	0	0
$778$	−1.61803	−1.61803
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	1.00000
$785$	0	0
$786$	0	0
$787$	2.00000	2.00000	1.00000			$0$
$787$	2.00000	2.00000	1.00000			$0$
$788$	0	0
$789$	0	0
$790$	−1.00000	−1.00000
$791$	0	0
$792$	0	0
$793$	−1.00000	−1.00000
$794$	0	0
$795$	0	0
$796$	2.00000	2.00000
$797$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$797$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$798$	0	0
$799$	0	0
$800$	0.618034	0.618034
$801$	0	0
$802$	0	0
$803$	−0.381966	−0.381966
$804$	0	0
$805$	0	0
$806$	1.00000	1.00000
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$811$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$812$	0	0
$813$	0	0
$814$	0.618034	0.618034
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−1.00000	−1.00000
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	−0.618034	−0.618034
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$829$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$830$	−1.23607	−1.23607
$831$	0	0
$832$	−1.61803	−1.61803
$833$	0	0
$834$	0	0
$835$	0.381966	0.381966
$836$	0	0
$837$	0	0
$838$	−1.61803	−1.61803
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.61803	1.61803
$842$	1.61803	1.61803
$843$	0	0
$844$	0.618034	0.618034
$845$	−1.00000	−1.00000
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	1.61803	1.61803
$852$	0	0
$853$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$853$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$854$	0	0
$855$	0	0
$856$	−1.61803	−1.61803
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	2.00000	2.00000
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	1.61803	1.61803
$867$	0	0
$868$	0	0
$869$	1.00000	1.00000
$870$	0	0
$871$	−1.00000	−1.00000
$872$	−2.00000	−2.00000
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	1.61803	1.61803
$879$	0	0
$880$	0.381966	0.381966
$881$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$881$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0.618034	0.618034
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	1.00000	1.00000
$900$	0	0
$901$	0	0
$902$	1.00000	1.00000
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−2.00000	−2.00000	−1.00000			$\pi$
$911$	−2.00000	−2.00000	−1.00000			$\pi$
$912$	0	0
$913$	1.23607	1.23607
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	2.00000	2.00000	1.00000			$0$
$919$	2.00000	2.00000	1.00000			$0$
$920$	1.00000	1.00000
$921$	0	0
$922$	2.00000	2.00000
$923$	0	0
$924$	0	0
$925$	−0.618034	−0.618034
$926$	1.61803	1.61803
$927$	0	0
$928$	−1.61803	−1.61803
$929$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$929$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$930$	0	0
$931$	0	0
$932$	1.61803	1.61803
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	2.61803	2.61803
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	−1.00000	−1.00000
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$953$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$954$	0	0
$955$	0.381966	0.381966
$956$	−0.618034	−0.618034
$957$	0	0
$958$	−1.61803	−1.61803
$959$	0	0
$960$	0	0
$961$	−0.618034	−0.618034
$962$	1.61803	1.61803
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$967$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$968$	0.618034	0.618034
$969$	0	0
$970$	0	0
$971$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$971$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$972$	0	0
$973$	0	0
$974$	−2.00000	−2.00000
$975$	0	0
$976$	0.618034	0.618034
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	−0.618034	−0.618034
$981$	0	0
$982$	−1.61803	−1.61803
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$991$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$992$	−0.618034	−0.618034
$993$	0	0
$994$	0	0
$995$	−1.23607	−1.23607
$996$	0	0
$997$	2.00000	2.00000	1.00000			$0$
$997$	2.00000	2.00000	1.00000			$0$
$998$	0	0
$999$	0	0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2664.1.m.a.739.1		2
3.2	odd	2		296.1.h.b.147.1	yes	2
8.3	odd	2		2664.1.m.b.739.2		2
12.11	even	2		1184.1.h.a.591.2		2
24.5	odd	2		1184.1.h.b.591.2		2
24.11	even	2		296.1.h.a.147.1	✓	2
37.36	even	2		2664.1.m.b.739.2		2
111.110	odd	2		296.1.h.a.147.1	✓	2
296.147	odd	2	CM	2664.1.m.a.739.1		2
444.443	even	2		1184.1.h.b.591.2		2
888.221	odd	2		1184.1.h.a.591.2		2
888.443	even	2		296.1.h.b.147.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.1.h.a.147.1	✓	2	24.11	even	2
296.1.h.a.147.1	✓	2	111.110	odd	2
296.1.h.b.147.1	yes	2	3.2	odd	2
296.1.h.b.147.1	yes	2	888.443	even	2
1184.1.h.a.591.2		2	12.11	even	2
1184.1.h.a.591.2		2	888.221	odd	2
1184.1.h.b.591.2		2	24.5	odd	2
1184.1.h.b.591.2		2	444.443	even	2
2664.1.m.a.739.1		2	1.1	even	1	trivial
2664.1.m.a.739.1		2	296.147	odd	2	CM
2664.1.m.b.739.2		2	8.3	odd	2
2664.1.m.b.739.2		2	37.36	even	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2664.1.m.a.739.1

Level	$2664$
Weight	$1$
Character	2664.739
Self dual	yes
Analytic conductor	$1.330$
Analytic rank	$0$
Dimension	$2$
Projective image	$D_{5}$
CM discriminant	-296
Inner twists	$2$