LMFDB - Embedded newform 2695.1.g.c.1814.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,1,Mod(1814,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2695.1814");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2695 = 5 \cdot 7^{2} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2695.g (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:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 55)
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(\sqrt{5}, \sqrt{-11})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.2.13475.1
Stark unit:	Root of $x^{4} - 6339x^{3} - 799x^{2} - 6339x + 1$

Embedding invariants

Embedding label			1814.1
Character	$\chi$	$=$	2695.1814

$q$ -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^{4} +1.00000 q^{5} +1.00000 q^{9} -1.00000 q^{11} +1.00000 q^{16} -1.00000 q^{20} +1.00000 q^{25} +2.00000 q^{31} -1.00000 q^{36} +1.00000 q^{44} +1.00000 q^{45} -1.00000 q^{55} -2.00000 q^{59} -1.00000 q^{64} +2.00000 q^{71} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{89} -1.00000 q^{99} +O(q^{100})

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$ .

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$1$	$-1$

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

)

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

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	−1.00000	−1.00000
$5$	1.00000	1.00000
$5$	1.00000	1.00000
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	1.00000	1.00000
$10$	0	0
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−1.00000	−1.00000
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	2.00000	2.00000	1.00000			$0$
$31$	2.00000	2.00000	1.00000			$0$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−1.00000	−1.00000
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	1.00000	1.00000
$45$	1.00000	1.00000
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	−1.00000	−1.00000
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−2.00000	−2.00000	−1.00000			$\pi$
$59$	−2.00000	−2.00000	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	−1.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	2.00000	2.00000	1.00000			$0$
$71$	2.00000	2.00000	1.00000			$0$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	1.00000	1.00000
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	2.00000	2.00000	1.00000			$0$
$89$	2.00000	2.00000	1.00000			$0$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	−1.00000	−1.00000
$100$	−1.00000	−1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	−2.00000	−2.00000
$125$	1.00000	1.00000
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	1.00000	1.00000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	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
$155$	2.00000	2.00000
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−1.00000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−1.00000
$177$	0	0
$178$	0	0
$179$	−2.00000	−2.00000	−1.00000			$\pi$
$179$	−2.00000	−2.00000	−1.00000			$\pi$
$180$	−1.00000	−1.00000
$181$	2.00000	2.00000	1.00000			$0$
$181$	2.00000	2.00000	1.00000			$0$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−2.00000	−2.00000	−1.00000			$\pi$
$191$	−2.00000	−2.00000	−1.00000			$\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−2.00000	−2.00000	−1.00000			$\pi$
$199$	−2.00000	−2.00000	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	1.00000	1.00000
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	1.00000	1.00000
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−2.00000	−2.00000	−1.00000			$\pi$
$229$	−2.00000	−2.00000	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	2.00000	2.00000
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−2.00000	−2.00000	−1.00000			$\pi$
$251$	−2.00000	−2.00000	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	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
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−2.00000	−2.00000	−1.00000			$\pi$
$269$	−2.00000	−2.00000	−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	0
$275$	−1.00000	−1.00000
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	2.00000	2.00000
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−2.00000	−2.00000
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−1.00000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−2.00000	−2.00000
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	−1.00000	−1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−1.00000	−1.00000
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−2.00000	−2.00000	−1.00000			$\pi$
$331$	−2.00000	−2.00000	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−2.00000	−2.00000
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	2.00000	2.00000
$356$	−2.00000	−2.00000
$357$	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	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	2.00000	2.00000	1.00000			$0$
$379$	2.00000	2.00000	1.00000			$0$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	2.00000	2.00000	1.00000			$0$
$389$	2.00000	2.00000	1.00000			$0$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	1.00000	1.00000
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	1.00000
$401$	−2.00000	−2.00000	−1.00000			$\pi$
$401$	−2.00000	−2.00000	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	1.00000	1.00000
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	2.00000	2.00000	1.00000			$0$
$419$	2.00000	2.00000	1.00000			$0$
$420$	0	0
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	2.00000	2.00000
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−2.00000	−2.00000	−1.00000			$\pi$
$449$	−2.00000	−2.00000	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	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	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−1.00000	−1.00000
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−1.00000	−1.00000
$496$	2.00000	2.00000
$497$	0	0
$498$	0	0
$499$	2.00000	2.00000	1.00000			$0$
$499$	2.00000	2.00000	1.00000			$0$
$500$	−1.00000	−1.00000
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	2.00000	2.00000	1.00000			$0$
$521$	2.00000	2.00000	1.00000			$0$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	1.00000
$530$	0	0
$531$	−2.00000	−2.00000
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	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
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−1.00000	−1.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	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
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−2.00000	−2.00000	−1.00000			$\pi$
$599$	−2.00000	−2.00000	−1.00000			$\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	1.00000	1.00000
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	2.00000	2.00000	1.00000			$0$
$619$	2.00000	2.00000	1.00000			$0$
$620$	−2.00000	−2.00000
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	2.00000	2.00000	1.00000			$0$
$631$	2.00000	2.00000	1.00000			$0$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	2.00000	2.00000
$640$	0	0
$641$	−2.00000	−2.00000	−1.00000			$\pi$
$641$	−2.00000	−2.00000	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	2.00000	2.00000
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	0	0
$676$	1.00000	1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−2.00000	−2.00000	−1.00000			$\pi$
$691$	−2.00000	−2.00000	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	1.00000	1.00000
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−2.00000	−2.00000	−1.00000			$\pi$
$709$	−2.00000	−2.00000	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	2.00000	2.00000
$717$	0	0
$718$	0	0
$719$	2.00000	2.00000	1.00000			$0$
$719$	2.00000	2.00000	1.00000			$0$
$720$	1.00000	1.00000
$721$	0	0
$722$	0	0
$723$	0	0
$724$	−2.00000	−2.00000
$725$	0	0
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	2.00000	2.00000	1.00000			$0$
$751$	2.00000	2.00000	1.00000			$0$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	2.00000	2.00000
$765$	0	0
$766$	0	0
$767$	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
$775$	2.00000	2.00000
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−2.00000	−2.00000
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	2.00000	2.00000
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	2.00000	2.00000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	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	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	2.00000	2.00000	1.00000			$0$
$829$	2.00000	2.00000	1.00000			$0$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−2.00000	−2.00000	−1.00000			$\pi$
$839$	−2.00000	−2.00000	−1.00000			$\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−1.00000	−1.00000
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	2.00000	2.00000	1.00000			$0$
$859$	2.00000	2.00000	1.00000			$0$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	−1.00000	−1.00000
$881$	−2.00000	−2.00000	−1.00000			$\pi$
$881$	−2.00000	−2.00000	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.00000	−1.00000
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−2.00000	−2.00000
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−1.00000	−1.00000
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	2.00000	2.00000
$906$	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
$913$	0	0
$914$	0	0
$915$	0	0
$916$	2.00000	2.00000
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−2.00000	−2.00000	−1.00000			$\pi$
$929$	−2.00000	−2.00000	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−2.00000	−2.00000
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	−2.00000	−2.00000
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	3.00000	3.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	2.00000	2.00000	1.00000			$0$
$971$	2.00000	2.00000	1.00000			$0$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	−2.00000	−2.00000
$980$	0	0
$981$	0	0
$982$	0	0
$983$	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
$991$	−2.00000	−2.00000	−1.00000			$\pi$
$991$	−2.00000	−2.00000	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−2.00000	−2.00000
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	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	2695.1.g.c.1814.1		1
5.4	even	2	RM	2695.1.g.c.1814.1		1
7.2	even	3		2695.1.q.b.2419.1		2
7.3	odd	6		2695.1.q.c.2529.1		2
7.4	even	3		2695.1.q.b.2529.1		2
7.5	odd	6		2695.1.q.c.2419.1		2
7.6	odd	2		55.1.d.a.54.1	✓	1
11.10	odd	2	CM	2695.1.g.c.1814.1		1
21.20	even	2		495.1.h.a.109.1		1
28.27	even	2		880.1.i.a.769.1		1
35.4	even	6		2695.1.q.b.2529.1		2
35.9	even	6		2695.1.q.b.2419.1		2
35.13	even	4		275.1.c.a.76.1		1
35.19	odd	6		2695.1.q.c.2419.1		2
35.24	odd	6		2695.1.q.c.2529.1		2
35.27	even	4		275.1.c.a.76.1		1
35.34	odd	2		55.1.d.a.54.1	✓	1
55.54	odd	2	CM	2695.1.g.c.1814.1		1
56.13	odd	2		3520.1.i.b.769.1		1
56.27	even	2		3520.1.i.a.769.1		1
77.6	even	10		605.1.h.a.239.1		4
77.10	even	6		2695.1.q.c.2529.1		2
77.13	even	10		605.1.h.a.524.1		4
77.20	odd	10		605.1.h.a.524.1		4
77.27	odd	10		605.1.h.a.239.1		4
77.32	odd	6		2695.1.q.b.2529.1		2
77.41	even	10		605.1.h.a.354.1		4
77.48	odd	10		605.1.h.a.94.1		4
77.54	even	6		2695.1.q.c.2419.1		2
77.62	even	10		605.1.h.a.94.1		4
77.65	odd	6		2695.1.q.b.2419.1		2
77.69	odd	10		605.1.h.a.354.1		4
77.76	even	2		55.1.d.a.54.1	✓	1
105.62	odd	4		2475.1.b.a.901.1		1
105.83	odd	4		2475.1.b.a.901.1		1
105.104	even	2		495.1.h.a.109.1		1
140.139	even	2		880.1.i.a.769.1		1
231.230	odd	2		495.1.h.a.109.1		1
280.69	odd	2		3520.1.i.b.769.1		1
280.139	even	2		3520.1.i.a.769.1		1
308.307	odd	2		880.1.i.a.769.1		1
385.13	odd	20		3025.1.x.a.1976.1		4
385.27	even	20		3025.1.x.a.2901.1		4
385.48	even	20		3025.1.x.a.2151.1		4
385.54	even	6		2695.1.q.c.2419.1		2
385.62	odd	20		3025.1.x.a.2151.1		4
385.69	odd	10		605.1.h.a.354.1		4
385.83	odd	20		3025.1.x.a.2901.1		4
385.97	even	20		3025.1.x.a.1976.1		4
385.104	odd	10		605.1.h.a.239.1		4
385.109	odd	6		2695.1.q.b.2529.1		2
385.118	odd	20		3025.1.x.a.1201.1		4
385.139	even	10		605.1.h.a.94.1		4
385.153	odd	4		275.1.c.a.76.1		1
385.164	even	6		2695.1.q.c.2529.1		2
385.167	odd	20		3025.1.x.a.1976.1		4
385.174	odd	10		605.1.h.a.524.1		4
385.202	even	20		3025.1.x.a.2151.1		4
385.219	odd	6		2695.1.q.b.2419.1		2
385.223	even	20		3025.1.x.a.1201.1		4
385.237	odd	20		3025.1.x.a.2901.1		4
385.244	even	10		605.1.h.a.524.1		4
385.258	even	20		3025.1.x.a.2901.1		4
385.272	odd	20		3025.1.x.a.1201.1		4
385.279	odd	10		605.1.h.a.94.1		4
385.293	odd	20		3025.1.x.a.2151.1		4
385.307	odd	4		275.1.c.a.76.1		1
385.314	even	10		605.1.h.a.239.1		4
385.328	even	20		3025.1.x.a.1976.1		4
385.349	even	10		605.1.h.a.354.1		4
385.377	even	20		3025.1.x.a.1201.1		4
385.384	even	2		55.1.d.a.54.1	✓	1
616.307	odd	2		3520.1.i.a.769.1		1
616.461	even	2		3520.1.i.b.769.1		1
1155.692	even	4		2475.1.b.a.901.1		1
1155.923	even	4		2475.1.b.a.901.1		1
1155.1154	odd	2		495.1.h.a.109.1		1
1540.1539	odd	2		880.1.i.a.769.1		1
3080.1539	odd	2		3520.1.i.a.769.1		1
3080.2309	even	2		3520.1.i.b.769.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.1.d.a.54.1	✓	1	7.6	odd	2
55.1.d.a.54.1	✓	1	35.34	odd	2
55.1.d.a.54.1	✓	1	77.76	even	2
55.1.d.a.54.1	✓	1	385.384	even	2
275.1.c.a.76.1		1	35.13	even	4
275.1.c.a.76.1		1	35.27	even	4
275.1.c.a.76.1		1	385.153	odd	4
275.1.c.a.76.1		1	385.307	odd	4
495.1.h.a.109.1		1	21.20	even	2
495.1.h.a.109.1		1	105.104	even	2
495.1.h.a.109.1		1	231.230	odd	2
495.1.h.a.109.1		1	1155.1154	odd	2
605.1.h.a.94.1		4	77.48	odd	10
605.1.h.a.94.1		4	77.62	even	10
605.1.h.a.94.1		4	385.139	even	10
605.1.h.a.94.1		4	385.279	odd	10
605.1.h.a.239.1		4	77.6	even	10
605.1.h.a.239.1		4	77.27	odd	10
605.1.h.a.239.1		4	385.104	odd	10
605.1.h.a.239.1		4	385.314	even	10
605.1.h.a.354.1		4	77.41	even	10
605.1.h.a.354.1		4	77.69	odd	10
605.1.h.a.354.1		4	385.69	odd	10
605.1.h.a.354.1		4	385.349	even	10
605.1.h.a.524.1		4	77.13	even	10
605.1.h.a.524.1		4	77.20	odd	10
605.1.h.a.524.1		4	385.174	odd	10
605.1.h.a.524.1		4	385.244	even	10
880.1.i.a.769.1		1	28.27	even	2
880.1.i.a.769.1		1	140.139	even	2
880.1.i.a.769.1		1	308.307	odd	2
880.1.i.a.769.1		1	1540.1539	odd	2
2475.1.b.a.901.1		1	105.62	odd	4
2475.1.b.a.901.1		1	105.83	odd	4
2475.1.b.a.901.1		1	1155.692	even	4
2475.1.b.a.901.1		1	1155.923	even	4
2695.1.g.c.1814.1		1	1.1	even	1	trivial
2695.1.g.c.1814.1		1	5.4	even	2	RM
2695.1.g.c.1814.1		1	11.10	odd	2	CM
2695.1.g.c.1814.1		1	55.54	odd	2	CM
2695.1.q.b.2419.1		2	7.2	even	3
2695.1.q.b.2419.1		2	35.9	even	6
2695.1.q.b.2419.1		2	77.65	odd	6
2695.1.q.b.2419.1		2	385.219	odd	6
2695.1.q.b.2529.1		2	7.4	even	3
2695.1.q.b.2529.1		2	35.4	even	6
2695.1.q.b.2529.1		2	77.32	odd	6
2695.1.q.b.2529.1		2	385.109	odd	6
2695.1.q.c.2419.1		2	7.5	odd	6
2695.1.q.c.2419.1		2	35.19	odd	6
2695.1.q.c.2419.1		2	77.54	even	6
2695.1.q.c.2419.1		2	385.54	even	6
2695.1.q.c.2529.1		2	7.3	odd	6
2695.1.q.c.2529.1		2	35.24	odd	6
2695.1.q.c.2529.1		2	77.10	even	6
2695.1.q.c.2529.1		2	385.164	even	6
3025.1.x.a.1201.1		4	385.118	odd	20
3025.1.x.a.1201.1		4	385.223	even	20
3025.1.x.a.1201.1		4	385.272	odd	20
3025.1.x.a.1201.1		4	385.377	even	20
3025.1.x.a.1976.1		4	385.13	odd	20
3025.1.x.a.1976.1		4	385.97	even	20
3025.1.x.a.1976.1		4	385.167	odd	20
3025.1.x.a.1976.1		4	385.328	even	20
3025.1.x.a.2151.1		4	385.48	even	20
3025.1.x.a.2151.1		4	385.62	odd	20
3025.1.x.a.2151.1		4	385.202	even	20
3025.1.x.a.2151.1		4	385.293	odd	20
3025.1.x.a.2901.1		4	385.27	even	20
3025.1.x.a.2901.1		4	385.83	odd	20
3025.1.x.a.2901.1		4	385.237	odd	20
3025.1.x.a.2901.1		4	385.258	even	20
3520.1.i.a.769.1		1	56.27	even	2
3520.1.i.a.769.1		1	280.139	even	2
3520.1.i.a.769.1		1	616.307	odd	2
3520.1.i.a.769.1		1	3080.1539	odd	2
3520.1.i.b.769.1		1	56.13	odd	2
3520.1.i.b.769.1		1	280.69	odd	2
3520.1.i.b.769.1		1	616.461	even	2
3520.1.i.b.769.1		1	3080.2309	even	2

Overview	Random
Universe	Knowledge

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	2695.1.g.c.1814.1

Level	$2695$
Weight	$1$
Character	2695.1814
Self dual	yes
Analytic conductor	$1.345$
Analytic rank	$0$
Dimension	$1$
Projective image	$D_{2}$
CM/RM discs	-11, -55, 5
Inner twists	$4$