LMFDB - Newform orbit 306.4.g.e

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [306,4,Mod(55,306)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(306, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("306.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$306 = 2 \cdot 3^{2} \cdot 17$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	306.g (of order $4$ , degree $2$ , 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:	no
Analytic conductor:	$18.0545844618$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 2x^{7} + 2x^{6} - 114x^{5} + 3058x^{4} - 12578x^{3} + 25538x^{2} + 8814x + 1521$ x^8 - 2x^7 + 2x^6 - 114x^5 + 3058x^4 - 12578x^3 + 25538x^2 + 8814*x + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{5}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Coefficients of the $q$ -expansion are expressed in terms of a basis $1,\beta_1,\ldots,\beta_{7}$ for the coefficient ring described below. We also show the integral $q$ -expansion of the trace form.

$f(q)$	$=$	$q - 2 \beta_{2} q^{2} - 4 q^{4} + (\beta_{5} + 2 \beta_{2} - 2) q^{5} + (\beta_{7} + \beta_{6} + \beta_{3} + \cdots + \beta_1) q^{7} + 8 \beta_{2} q^{8} + ( - 2 \beta_{7} + 4 \beta_{2} + 4) q^{10} + (2 \beta_{7} + \beta_{6} - \beta_{3} + \cdots - 1) q^{11}+ \cdots + ( - 4 \beta_{7} - 20 \beta_{6} + \cdots - 194) q^{98}+O(q^{100})$ q - 2b2 q^2 - 4 * q^4 + (b5 + 2b2 - 2) q^5 + (b7 + b6 + b3 - b2 + b1) * q^7 + 8b2 q^8 + (-2b7 + 4b2 + 4) * q^10 + (2b7 + b6 - b3 - 2b2 - b1 - 1) * q^11 + (-b6 + b4 + b2 - 3b1 - 6) q^13 + (2b5 - 2b4 - 2b3 + 2b1) * q^14 + 16 * q^16 + (4b6 - b4 + b3 - 5b2 - 4b1 + 4) q^17 + (-5b6 - 5b4 - 5b3 - 15b2) * q^19 + (-4b5 - 8b2 + 8) * q^20 + (4b5 - 2b4 + 2b3 + 2b2 - 2b1 - 2) q^22 + (-7b7 - 7b3 - 5b2 - 7b1 - 5) * q^23 + (7b7 - 4b6 - 7b5 - 4b4 + 5b3 + 11b2) * q^25 + (2b6 + 2b4 + 6b3 + 10b2) * q^26 + (-4b7 - 4b6 - 4b3 + 4b2 - 4b1) q^28 + (-9b5 - 11b4 - 9b3 - b2 + 9b1 + 1) * q^29 + (3b5 - b4 + 16b3 - 18b2 - 16b1 + 18) * q^31 - 32b2 q^32 + (-2b6 - 8b4 + 8b3 - 6b2 + 2b1 - 2) q^34 + (-3b7 + 2b6 - 3b5 - 2b4 - 2b2 - 4b1 + 64) * q^35 + (-7b5 - 11b4 + 12b3 + 5b2 - 12b1 - 5) q^37 + (-10b6 + 10b4 + 10b2 - 10b1 - 40) * q^38 + (8b7 - 16b2 - 16) * q^40 + (14b7 + 21b6 + 12b3 + 35b2 + 12b1 + 56) q^41 + (-23b7 - 16b6 + 23b5 - 16b4 + b3 + 110b2) q^43 + (-8b7 - 4b6 + 4b3 + 8b2 + 4b1 + 4) q^44 + (-14b5 + 14b3 + 10b2 - 14b1 - 10) * q^46 + (13b7 - 3b6 + 13b5 + 3b4 + 3b2 - 16b1 - 168) * q^47 + (-2b7 - 10b6 + 2b5 - 10b4 + 4b3 - 87b2) * q^49 + (14b7 - 8b6 + 14b5 + 8b4 + 8b2 + 10b1 + 14) * q^50 + (4b6 - 4b4 - 4b2 + 12b1 + 24) * q^52 + (-21b7 - 17b6 + 21b5 - 17b4 - 36b3 + 77b2) * q^53 + (3b7 + 8b6 + 3b5 - 8b4 - 8b2 - 9b1 + 190) * q^55 + (-8b5 + 8b4 + 8b3 - 8b1) * q^56 + (18b7 - 22b6 - 18b3 + 20b2 - 18b1 - 2) q^58 + (-b7 + 12b6 + b5 + 12b4 + 16b3 - 76b2) * q^59 + (19b7 - 19b6 - 12b3 - 52b2 - 12b1 - 71) q^61 + (-6b7 - 2b6 + 32b3 - 34b2 + 32b1 - 36) q^62 - 64 * q^64 + (-4b5 - 5b4 + b3 - 61b2 - b1 + 61) q^65 + (-19b7 - 9b6 - 19b5 + 9b4 + 9b2 - 24b1 - 42) * q^67 + (-16b6 + 4b4 - 4b3 + 20b2 + 16b1 - 16) q^68 + (6b7 - 4b6 - 6b5 - 4b4 + 8b3 - 124b2) * q^70 + (3b5 + 9b4 + 8b3 - 38b2 - 8b1 + 38) q^71 + (-22b5 - 4b4 + b3 + 63b2 - b1 - 63) q^73 + (14b7 - 22b6 + 24b3 + 32b2 + 24b1 + 10) q^74 + (20b6 + 20b4 + 20b3 + 60b2) * q^76 + (-3b6 - 3b4 - 34b3 + 65b2) * q^77 + (-17b7 + 19b6 + 35b3 + 173b2 + 35b1 + 192) q^79 + (16b5 + 32b2 - 32) * q^80 + (28b5 - 42b4 - 24b3 - 112b2 + 24b1 + 112) q^82 + (53b7 + 15b6 - 53b5 + 15b4 + 34b3 - 81b2) * q^83 + (17b7 - 4b6 + 68b5 + b4 - b3 + 39b2 + 4b1 - 157) q^85 + (-46b7 - 32b6 - 46b5 + 32b4 + 32b2 + 2b1 + 188) * q^86 + (-16b5 + 8b4 - 8b3 - 8b2 + 8b1 + 8) q^88 + (-42b7 - 15b6 - 42b5 + 15b4 + 15b2 - 90b1 - 282) * q^89 + (-2b7 + 24b6 - 19b3 - 268b2 - 19b1 - 244) q^91 + (28b7 + 28b3 + 20b2 + 28b1 + 20) * q^92 + (-26b7 + 6b6 + 26b5 + 6b4 + 32b3 + 330b2) * q^94 + (-70b7 + 15b6 - 5b3 + 240b2 - 5b1 + 255) q^95 + (-52b5 + 10b4 - 13b3 - 65b2 + 13b1 + 65) q^97 + (-4b7 - 20b6 - 4b5 + 20b4 + 20b2 + 8b1 - 194) * q^98
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 32 q^{4} - 16 q^{5} - 8 q^{7} + 32 q^{10} - 8 q^{11} - 28 q^{13} - 16 q^{14} + 128 q^{16} + 28 q^{17} + 64 q^{20} - 16 q^{22} - 12 q^{23} + 32 q^{28} - 72 q^{29} + 204 q^{31} - 48 q^{34} + 512 q^{35}+ \cdots - 1424 q^{98}+O(q^{100})$ 8 * q - 32 * q^4 - 16 * q^5 - 8 * q^7 + 32 * q^10 - 8 * q^11 - 28 * q^13 - 16 * q^14 + 128 * q^16 + 28 * q^17 + 64 * q^20 - 16 * q^22 - 12 * q^23 + 32 * q^28 - 72 * q^29 + 204 * q^31 - 48 * q^34 + 512 * q^35 - 36 * q^37 - 200 * q^38 - 128 * q^40 + 316 * q^41 + 32 * q^44 - 24 * q^46 - 1256 * q^47 + 136 * q^50 + 112 * q^52 + 1492 * q^55 + 64 * q^56 + 144 * q^58 - 444 * q^61 - 408 * q^62 - 512 * q^64 + 472 * q^65 - 168 * q^67 - 112 * q^68 + 372 * q^71 - 516 * q^73 + 72 * q^74 + 1320 * q^79 - 256 * q^80 + 632 * q^82 - 1252 * q^85 + 1752 * q^86 + 64 * q^88 - 1776 * q^89 - 1972 * q^91 + 48 * q^92 + 2000 * q^95 + 508 * q^97 - 1424 * q^98

Basis of coefficient ring in terms of a root $\nu$ of $x^{8} - 2x^{7} + 2x^{6} - 114x^{5} + 3058x^{4} - 12578x^{3} + 25538x^{2} + 8814x + 1521$ x^8 - 2*x^7 + 2*x^6 - 114*x^5 + 3058*x^4 - 12578*x^3 + 25538*x^2 + 8814*x + 1521 :

$\beta_{1}$	$=$	$( 4685 \nu^{7} + 2245 \nu^{6} - 134895 \nu^{5} - 1704897 \nu^{4} + 6165305 \nu^{3} + \cdots - 728296605 ) / 171478116$ (4685v^7 + 2245v^6 - 134895v^5 - 1704897v^4 + 6165305v^3 - 16239995v^2 - 5511675*v - 728296605) / 171478116
$\beta_{2}$	$=$	$( 573587 \nu^{7} - 1343851 \nu^{6} + 1157275 \nu^{5} - 65778099 \nu^{4} + 1776591443 \nu^{3} + \cdots + 2542582029 ) / 2972287344$ (573587v^7 - 1343851v^6 + 1157275v^5 - 65778099v^4 + 1776591443v^3 - 7824210427v^2 + 15986256955*v + 2542582029) / 2972287344
$\beta_{3}$	$=$	$( - 3574617 \nu^{7} + 9311953 \nu^{6} - 3031185 \nu^{5} + 414187389 \nu^{4} - 11322797793 \nu^{3} + \cdots - 16174502019 ) / 4458431016$ (-3574617v^7 + 9311953v^6 - 3031185v^5 + 414187389v^4 - 11322797793v^3 + 49831461001v^2 - 101696732985*v - 16174502019) / 4458431016
$\beta_{4}$	$=$	$( 13031969 \nu^{7} - 29500033 \nu^{6} + 59401281 \nu^{5} - 1434249369 \nu^{4} + 40305176801 \nu^{3} + \cdots - 9776855673 ) / 8916862032$ (13031969v^7 - 29500033v^6 + 59401281v^5 - 1434249369v^4 + 40305176801v^3 - 178060596481v^2 + 448815663633*v - 9776855673) / 8916862032
$\beta_{5}$	$=$	$( 719387 \nu^{7} - 1691371 \nu^{6} + 2114511 \nu^{5} - 82844019 \nu^{4} + 2228522843 \nu^{3} + \cdots - 538852275 ) / 342956232$ (719387v^7 - 1691371v^6 + 2114511v^5 - 82844019v^4 + 2228522843v^3 - 9811360267v^2 + 21857550135*v - 538852275) / 342956232
$\beta_{6}$	$=$	$( 10503593 \nu^{7} - 16644633 \nu^{6} + 21282045 \nu^{5} - 1217713977 \nu^{4} + \cdots + 79022574423 ) / 4458431016$ (10503593v^7 - 16644633v^6 + 21282045v^5 - 1217713977v^4 + 31563532001v^3 - 120269076081v^2 + 241700002845*v + 79022574423) / 4458431016
$\beta_{7}$	$=$	$( - 850429 \nu^{7} + 1686369 \nu^{6} - 1693353 \nu^{5} + 96528105 \nu^{4} - 2595266053 \nu^{3} + \cdots - 7447081239 ) / 342956232$ (-850429v^7 + 1686369v^6 - 1693353v^5 + 96528105v^4 - 2595266053v^3 + 10629054849v^2 - 21577168137*v - 7447081239) / 342956232

Display $\nu^j$ in terms of $\beta_i$

$\nu$	$=$	$( -\beta_{5} + \beta_{4} - \beta_{3} - \beta_{2} + \beta _1 + 1 ) / 4$ (-b5 + b4 - b3 - b2 + b1 + 1) / 4
$\nu^{2}$	$=$	$( -7\beta_{7} - 3\beta_{6} + 7\beta_{5} - 3\beta_{4} - 2\beta_{3} - 115\beta_{2} ) / 4$ (-7b7 - 3b6 + 7b5 - 3b4 - 2b3 - 115b2) / 4
$\nu^{3}$	$=$	$( 65\beta_{7} + 41\beta_{6} - 53\beta_{3} + 122\beta_{2} - 53\beta _1 + 163 ) / 4$ (65b7 + 41b6 - 53b3 + 122b2 - 53*b1 + 163) / 4
$\nu^{4}$	$=$	$-110\beta_{7} - 60\beta_{6} - 110\beta_{5} + 60\beta_{4} + 60\beta_{2} + 2\beta _1 - 1475$ -110b7 - 60b6 - 110b5 + 60b4 + 60b2 + 2b1 - 1475
$\nu^{5}$	$=$	$( 4303\beta_{5} - 2455\beta_{4} + 2695\beta_{3} - 16601\beta_{2} - 2695\beta _1 + 16601 ) / 4$ (4303b5 - 2455b4 + 2695b3 - 16601b2 - 2695*b1 + 16601) / 4
$\nu^{6}$	$=$	$( 27409\beta_{7} + 15501\beta_{6} - 27409\beta_{5} + 15501\beta_{4} - 7114\beta_{3} + 313933\beta_{2} ) / 4$ (27409b7 + 15501b6 - 27409b5 + 15501b4 - 7114b3 + 313933b2) / 4
$\nu^{7}$	$=$	$( -283055\beta_{7} - 159119\beta_{6} + 142643\beta_{3} - 1101446\beta_{2} + 142643\beta _1 - 1260565 ) / 4$ (-283055b7 - 159119b6 + 142643b3 - 1101446b2 + 142643*b1 - 1260565) / 4

Display $\beta_i$ in terms of $\nu^j$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/306\mathbb{Z}\right)^\times$ .

$n$	$37$	$137$
$\chi(n)$	$-\beta_{2}$	$1$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

\iota_m(\nu)

a_{2}

a_{3}

a_{4}

a_{5}

a_{6}

a_{7}

a_{8}

a_{9}

a_{10}

55.1

−0.159969	+	0.159969i
4.33285	−	4.33285i
2.48586	−	2.48586i
−5.65874	+	5.65874i
−0.159969	−	0.159969i
4.33285	+	4.33285i
2.48586	+	2.48586i
−5.65874	−	5.65874i

−

2.00000i

−4.00000

−13.7126

13.7126i

−6.84354

−

6.84354i

8.00000i

27.4252

27.4252i

55.2

−

2.00000i

−4.00000

−0.580334

0.580334i

13.3735

13.3735i

8.00000i

1.16067

1.16067i

55.3

−

2.00000i

−4.00000

−0.376810

0.376810i

−15.9157

−

15.9157i

8.00000i

0.753619

0.753619i

55.4

−

2.00000i

−4.00000

6.66975

−

6.66975i

5.38568

5.38568i

8.00000i

−13.3395

−

13.3395i

217.1

2.00000i

−4.00000

−13.7126

−

13.7126i

−6.84354

6.84354i

−

8.00000i

27.4252

−

27.4252i

217.2

2.00000i

−4.00000

−0.580334

−

0.580334i

13.3735

−

13.3735i

−

8.00000i

1.16067

−

1.16067i

217.3

2.00000i

−4.00000

−0.376810

−

0.376810i

−15.9157

15.9157i

−

8.00000i

0.753619

−

0.753619i

217.4

2.00000i

−4.00000

6.66975

6.66975i

5.38568

−

5.38568i

−

8.00000i

−13.3395

13.3395i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.c	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	306.4.g.e	✓	8
3.b	odd	2	1		306.4.g.f	yes	8
17.c	even	4	1	inner	306.4.g.e	✓	8
51.f	odd	4	1		306.4.g.f	yes	8

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
306.4.g.e	✓	8	1.a	even	1	1	trivial
306.4.g.e	✓	8	17.c	even	4	1	inner
306.4.g.f	yes	8	3.b	odd	2	1
306.4.g.f	yes	8	51.f	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5}^{8} + 16T_{5}^{7} + 128T_{5}^{6} - 2360T_{5}^{5} + 28721T_{5}^{4} + 59416T_{5}^{3} + 59168T_{5}^{2} + 27520T_{5} + 6400$ T5^8 + 16*T5^7 + 128*T5^6 - 2360*T5^5 + 28721*T5^4 + 59416*T5^3 + 59168*T5^2 + 27520*T5 + 6400 acting on $S_{4}^{\mathrm{new}}(306, [\chi])$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$(T^{2} + 4)^{4}$ (T^2 + 4)^4
$3$	$T^{8}$ T^8
$5$	$T^{8} + 16 T^{7} + \cdots + 6400$ T^8 + 16T^7 + 128T^6 - 2360T^5 + 28721T^4 + 59416T^3 + 59168T^2 + 27520*T + 6400
$7$	$T^{8} + 8 T^{7} + \cdots + 984704400$ T^8 + 8T^7 + 32T^6 - 2320T^5 + 179304T^4 + 544032T^3 + 1305728T^2 - 50710080*T + 984704400
$11$	$T^{8} + \cdots + 33694273600$ T^8 + 8T^7 + 32T^6 + 33040T^5 + 2352401T^4 + 63904088T^3 + 981776672T^2 + 8133910720*T + 33694273600
$13$	$(T^{4} + 14 T^{3} + \cdots + 162420)^{2}$ (T^4 + 14T^3 - 1547T^2 - 3988*T + 162420)^2
$17$	$T^{8} + \cdots + 582622237229761$ T^8 - 28T^7 - 13770T^6 + 135252T^5 + 87736354T^4 + 664493076T^3 - 332374325130T^2 - 3320460541916*T + 582622237229761
$19$	$T^{8} + \cdots + 704371600000000$ T^8 + 32450T^6 + 303070625T^4 + 944888000000*T^2 + 704371600000000
$23$	$T^{8} + \cdots + 548769824100$ T^8 + 12T^7 + 72T^6 - 621736T^5 + 651372021T^4 - 8060622804T^3 + 49651567688T^2 + 233440707960*T + 548769824100
$29$	$T^{8} + \cdots + 13\!\cdots\!00$ T^8 + 72T^7 + 2592T^6 - 4328320T^5 + 4761293056T^4 + 61871194112T^3 + 1480631386112T^2 - 1976715588403200*T + 1319506176245760000
$31$	$T^{8} + \cdots + 43\!\cdots\!16$ T^8 - 204T^7 + 20808T^6 - 4621208T^5 + 8269137508T^4 - 1937246407616T^3 + 233811835576832T^2 - 14292946928658432*T + 436864822093910016
$37$	$T^{8} + \cdots + 82\!\cdots\!00$ T^8 + 36T^7 + 648T^6 - 552168T^5 + 11353630084T^4 + 439690110048T^3 + 8624136417408T^2 - 11897361145981440*T + 8206456588058649600
$41$	$T^{8} + \cdots + 15\!\cdots\!00$ T^8 - 316T^7 + 49928T^6 - 9326368T^5 + 16018521749T^4 - 5757574120660T^3 + 1063111238280200T^2 - 56899383852229000*T + 1522672212552602500
$43$	$T^{8} + \cdots + 11\!\cdots\!00$ T^8 + 599698T^6 + 118255045201T^4 + 8169909510887584*T^2 + 114694049956148640000
$47$	$(T^{4} + 628 T^{3} + \cdots + 388464032)^{2}$ (T^4 + 628T^3 + 15708T^2 - 27526144*T + 388464032)^2
$53$	$T^{8} + \cdots + 31\!\cdots\!84$ T^8 + 730328T^6 + 173327339600T^4 + 15102038102086912*T^2 + 318280923745406198784
$59$	$T^{8} + \cdots + 20\!\cdots\!00$ T^8 + 241860T^6 + 6649135428T^4 + 63368764695424*T^2 + 200375410120934400
$61$	$T^{8} + \cdots + 47\!\cdots\!76$ T^8 + 444T^7 + 98568T^6 - 60546808T^5 + 40137898884T^4 + 6821438522592T^3 + 905364266327168T^2 - 293224555802989056*T + 47484003579388978176
$67$	$(T^{4} + 84 T^{3} + \cdots + 8186232960)^{2}$ (T^4 + 84T^3 - 194972T^2 - 6924512*T + 8186232960)^2
$71$	$T^{8} + \cdots + 23\!\cdots\!00$ T^8 - 372T^7 + 69192T^6 + 2158488T^5 - 47141644T^4 - 4410603264T^3 + 7232104268928T^2 + 578035135117440*T + 23100096804865600
$73$	$T^{8} + \cdots + 14\!\cdots\!00$ T^8 + 516T^7 + 133128T^6 + 18867976T^5 + 13279942404T^4 + 6308597176832T^3 + 1665304230053888T^2 + 219683300111165440*T + 14490070786096153600
$79$	$T^{8} + \cdots + 14\!\cdots\!00$ T^8 - 1320T^7 + 871200T^6 + 29114640T^5 - 31287639896T^4 - 3534871270560T^3 + 32347653085699200T^2 + 9844002641802024000*T + 1497858094296280890000
$83$	$T^{8} + \cdots + 34\!\cdots\!00$ T^8 + 2345104T^6 + 1603019630400T^4 + 406224268314880000*T^2 + 34056470219778304000000
$89$	$(T^{4} + 888 T^{3} + \cdots + 154468827360)^{2}$ (T^4 + 888T^3 - 1413522T^2 - 160316496*T + 154468827360)^2
$97$	$T^{8} + \cdots + 36\!\cdots\!00$ T^8 - 508T^7 + 129032T^6 - 50043816T^5 + 377240749636T^4 - 211010279382304T^3 + 59769285279099008T^2 - 6641151558498996480*T + 368959523415757574400
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Overview	Random
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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 $\F_{q}$
Belyi maps

$n$ :		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 55.4
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

$q$ -expansion

Character values

Embeddings

Inner twists

Twists

Hecke kernels

Hecke characteristic polynomials

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	306.4.g.e

Level	$306$
Weight	$4$
Character orbit	306.g
Analytic conductor	$18.055$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$