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Properties

Label 968.2.c.h
Level 968968
Weight 22
Character orbit 968.c
Analytic conductor 7.7307.730
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [968,2,Mod(485,968)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(968, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("968.485");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 968=23⋅112 968 = 2^{3} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 968.c (of order 22, degree 11, 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: 7.729518915667.72951891566
Analytic rank: 00
Dimension: 2020
Coefficient field: Q[x]/(x20−⋯ )\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20−x18−2x16−2x15−4x14−4x13+12x12+16x11+32x9+⋯+1024 x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,…,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

Coefficients of the qq-expansion are expressed in terms of a basis 1,β1,…,β191,\beta_1,\ldots,\beta_{19} for the coefficient ring described below. We also show the integral qq-expansion of the trace form.

f(q)f(q) == q−β15q2+β10q3−β4q4+β6q5−β11q6+(β17+1)q7+(β19+β16+⋯+β4)q8+(β16−β11+β3)q9+⋯+(−β17−β16+β14+⋯−3)q98+O(q100) q - \beta_{15} q^{2} + \beta_{10} q^{3} - \beta_{4} q^{4} + \beta_{6} q^{5} - \beta_{11} q^{6} + (\beta_{17} + 1) q^{7} + (\beta_{19} + \beta_{16} + \cdots + \beta_{4}) q^{8} + (\beta_{16} - \beta_{11} + \beta_{3}) q^{9}+ \cdots + ( - \beta_{17} - \beta_{16} + \beta_{14} + \cdots - 3) q^{98}+O(q^{100}) Copy content Toggle raw display
Tr⁡(f)(q)\operatorname{Tr}(f)(q) == 20q+2q4−q6+10q7−10q9−10q10−3q12−4q14−4q15+10q16+2q17−5q18−16q20−4q23+15q24−2q25+30q26−14q28+16q30+⋯−72q98+O(q100) 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) Copy content Toggle raw display

Basis of coefficient ring in terms of a root ν\nu of x20−x18−2x16−2x15−4x14−4x13+12x12+16x11+32x9+⋯+1024 x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 : Copy content Toggle raw display

β1\beta_{1}== ν2+ν \nu^{2} + \nu Copy content Toggle raw display
β2\beta_{2}== −ν2+ν -\nu^{2} + \nu Copy content Toggle raw display
β3\beta_{3}== (−3ν19+10ν18+39ν17+30ν16+18ν15−86ν14−128ν13+⋯−2560)/12288 ( - 3 \nu^{19} + 10 \nu^{18} + 39 \nu^{17} + 30 \nu^{16} + 18 \nu^{15} - 86 \nu^{14} - 128 \nu^{13} + \cdots - 2560 ) / 12288 Copy content Toggle raw display
β4\beta_{4}== (ν18−ν16−2ν14−2ν13−4ν12−4ν11+12ν10+16ν9+⋯−256)/256 ( \nu^{18} - \nu^{16} - 2 \nu^{14} - 2 \nu^{13} - 4 \nu^{12} - 4 \nu^{11} + 12 \nu^{10} + 16 \nu^{9} + \cdots - 256 ) / 256 Copy content Toggle raw display
β5\beta_{5}== (−ν19−10ν18−15ν17−6ν16−22ν15−26ν14+80ν13+⋯−512)/3072 ( - \nu^{19} - 10 \nu^{18} - 15 \nu^{17} - 6 \nu^{16} - 22 \nu^{15} - 26 \nu^{14} + 80 \nu^{13} + \cdots - 512 ) / 3072 Copy content Toggle raw display
β6\beta_{6}== (3ν19+2ν18+9ν17+6ν16+30ν15+14ν14+8ν13+⋯+2560)/3072 ( 3 \nu^{19} + 2 \nu^{18} + 9 \nu^{17} + 6 \nu^{16} + 30 \nu^{15} + 14 \nu^{14} + 8 \nu^{13} + \cdots + 2560 ) / 3072 Copy content Toggle raw display
β7\beta_{7}== (ν19+2ν18−ν17−2ν16+6ν15−6ν14+20ν12+4ν11+⋯+512)/1024 ( \nu^{19} + 2 \nu^{18} - \nu^{17} - 2 \nu^{16} + 6 \nu^{15} - 6 \nu^{14} + 20 \nu^{12} + 4 \nu^{11} + \cdots + 512 ) / 1024 Copy content Toggle raw display
β8\beta_{8}== (ν19+2ν18+3ν17+6ν16+10ν15+18ν14−4ν12−28ν11+⋯−512)/1024 ( \nu^{19} + 2 \nu^{18} + 3 \nu^{17} + 6 \nu^{16} + 10 \nu^{15} + 18 \nu^{14} - 4 \nu^{12} - 28 \nu^{11} + \cdots - 512 ) / 1024 Copy content Toggle raw display
β9\beta_{9}== (−7ν19+10ν18−21ν17−18ν16+26ν15+66ν14+16ν13+⋯+3584)/6144 ( - 7 \nu^{19} + 10 \nu^{18} - 21 \nu^{17} - 18 \nu^{16} + 26 \nu^{15} + 66 \nu^{14} + 16 \nu^{13} + \cdots + 3584 ) / 6144 Copy content Toggle raw display
β10\beta_{10}== (5ν19−6ν18−ν17−18ν16−30ν15−6ν14−52ν12+⋯−2560)/4096 ( 5 \nu^{19} - 6 \nu^{18} - \nu^{17} - 18 \nu^{16} - 30 \nu^{15} - 6 \nu^{14} - 52 \nu^{12} + \cdots - 2560 ) / 4096 Copy content Toggle raw display
β11\beta_{11}== (−5ν19−10ν18+17ν17+2ν16+46ν15+70ν14+32ν13+⋯+6656)/4096 ( - 5 \nu^{19} - 10 \nu^{18} + 17 \nu^{17} + 2 \nu^{16} + 46 \nu^{15} + 70 \nu^{14} + 32 \nu^{13} + \cdots + 6656 ) / 4096 Copy content Toggle raw display
β12\beta_{12}== (−15ν19−46ν18−45ν17−42ν16+42ν15+50ν14+128ν13+⋯+24064)/12288 ( - 15 \nu^{19} - 46 \nu^{18} - 45 \nu^{17} - 42 \nu^{16} + 42 \nu^{15} + 50 \nu^{14} + 128 \nu^{13} + \cdots + 24064 ) / 12288 Copy content Toggle raw display
β13\beta_{13}== (−5ν19+6ν18−3ν17−6ν16+10ν15−2ν14+48ν13+⋯+4608)/3072 ( - 5 \nu^{19} + 6 \nu^{18} - 3 \nu^{17} - 6 \nu^{16} + 10 \nu^{15} - 2 \nu^{14} + 48 \nu^{13} + \cdots + 4608 ) / 3072 Copy content Toggle raw display
β14\beta_{14}== (−23ν19−30ν18−21ν17+6ν16+10ν15+34ν14+192ν13+⋯+7680)/12288 ( - 23 \nu^{19} - 30 \nu^{18} - 21 \nu^{17} + 6 \nu^{16} + 10 \nu^{15} + 34 \nu^{14} + 192 \nu^{13} + \cdots + 7680 ) / 12288 Copy content Toggle raw display
β15\beta_{15}== (ν19−ν17−2ν15−2ν14−4ν13−4ν12+12ν11+16ν10+⋯−256ν)/512 ( \nu^{19} - \nu^{17} - 2 \nu^{15} - 2 \nu^{14} - 4 \nu^{13} - 4 \nu^{12} + 12 \nu^{11} + 16 \nu^{10} + \cdots - 256 \nu ) / 512 Copy content Toggle raw display
β16\beta_{16}== (−27ν19−70ν18−81ν17−18ν16+114ν15+314ν14+⋯+30208)/12288 ( - 27 \nu^{19} - 70 \nu^{18} - 81 \nu^{17} - 18 \nu^{16} + 114 \nu^{15} + 314 \nu^{14} + \cdots + 30208 ) / 12288 Copy content Toggle raw display
β17\beta_{17}== (ν19+ν15−2ν14−6ν13−6ν12−12ν11+4ν10+12ν9+⋯−384)/384 ( \nu^{19} + \nu^{15} - 2 \nu^{14} - 6 \nu^{13} - 6 \nu^{12} - 12 \nu^{11} + 4 \nu^{10} + 12 \nu^{9} + \cdots - 384 ) / 384 Copy content Toggle raw display
β18\beta_{18}== (−47ν19−78ν18−45ν17−42ν16+10ν15+274ν14+384ν13+⋯+19968)/12288 ( - 47 \nu^{19} - 78 \nu^{18} - 45 \nu^{17} - 42 \nu^{16} + 10 \nu^{15} + 274 \nu^{14} + 384 \nu^{13} + \cdots + 19968 ) / 12288 Copy content Toggle raw display
β19\beta_{19}== (37ν19+34ν18+15ν17+54ν16−14ν15−166ν14−368ν13+⋯−27136)/6144 ( 37 \nu^{19} + 34 \nu^{18} + 15 \nu^{17} + 54 \nu^{16} - 14 \nu^{15} - 166 \nu^{14} - 368 \nu^{13} + \cdots - 27136 ) / 6144 Copy content Toggle raw display

Display νj\nu^j in terms of βi\beta_i

ν\nu== (β2+β1)/2 ( \beta_{2} + \beta_1 ) / 2 Copy content Toggle raw display
ν2\nu^{2}== (−β2+β1)/2 ( -\beta_{2} + \beta_1 ) / 2 Copy content Toggle raw display
ν3\nu^{3}== (−2β18+2β16−2β15+2β12−2β11+2β10+⋯−β1)/2 ( - 2 \beta_{18} + 2 \beta_{16} - 2 \beta_{15} + 2 \beta_{12} - 2 \beta_{11} + 2 \beta_{10} + \cdots - \beta_1 ) / 2 Copy content Toggle raw display
ν4\nu^{4}== (2β18+2β17−2β14+2β13−2β11−2β7+2β6+⋯+β1)/2 ( 2 \beta_{18} + 2 \beta_{17} - 2 \beta_{14} + 2 \beta_{13} - 2 \beta_{11} - 2 \beta_{7} + 2 \beta_{6} + \cdots + \beta_1 ) / 2 Copy content Toggle raw display
ν5\nu^{5}== (2β18−2β17−2β14−2β13−2β11+2β7+2β6+⋯+β1)/2 ( 2 \beta_{18} - 2 \beta_{17} - 2 \beta_{14} - 2 \beta_{13} - 2 \beta_{11} + 2 \beta_{7} + 2 \beta_{6} + \cdots + \beta_1 ) / 2 Copy content Toggle raw display
ν6\nu^{6}== (−2β18+2β17−4β15+2β14+2β13+4β12−2β11+⋯+4)/2 ( - 2 \beta_{18} + 2 \beta_{17} - 4 \beta_{15} + 2 \beta_{14} + 2 \beta_{13} + 4 \beta_{12} - 2 \beta_{11} + \cdots + 4 ) / 2 Copy content Toggle raw display
ν7\nu^{7}== (4β19+2β18−2β17+4β15+10β14+2β13+2β11+⋯+8)/2 ( 4 \beta_{19} + 2 \beta_{18} - 2 \beta_{17} + 4 \beta_{15} + 10 \beta_{14} + 2 \beta_{13} + 2 \beta_{11} + \cdots + 8 ) / 2 Copy content Toggle raw display
ν8\nu^{8}== (−4β19−6β18−2β17−4β15−6β14−6β13+8β12+⋯−8)/2 ( - 4 \beta_{19} - 6 \beta_{18} - 2 \beta_{17} - 4 \beta_{15} - 6 \beta_{14} - 6 \beta_{13} + 8 \beta_{12} + \cdots - 8 ) / 2 Copy content Toggle raw display
ν9\nu^{9}== (−4β19+2β18+6β17+4β15+10β14−6β13−8β12+⋯+8)/2 ( - 4 \beta_{19} + 2 \beta_{18} + 6 \beta_{17} + 4 \beta_{15} + 10 \beta_{14} - 6 \beta_{13} - 8 \beta_{12} + \cdots + 8 ) / 2 Copy content Toggle raw display
ν10\nu^{10}== (−4β19+10β18+6β17+8β16+12β15−14β14+⋯+β1)/2 ( - 4 \beta_{19} + 10 \beta_{18} + 6 \beta_{17} + 8 \beta_{16} + 12 \beta_{15} - 14 \beta_{14} + \cdots + \beta_1 ) / 2 Copy content Toggle raw display
ν11\nu^{11}== (4β19+10β18−10β17−8β16+28β15+2β14+18β13+⋯−32)/2 ( 4 \beta_{19} + 10 \beta_{18} - 10 \beta_{17} - 8 \beta_{16} + 28 \beta_{15} + 2 \beta_{14} + 18 \beta_{13} + \cdots - 32 ) / 2 Copy content Toggle raw display
ν12\nu^{12}== (−20β19−6β18+6β17−8β16+12β15+34β14+⋯−32)/2 ( - 20 \beta_{19} - 6 \beta_{18} + 6 \beta_{17} - 8 \beta_{16} + 12 \beta_{15} + 34 \beta_{14} + \cdots - 32 ) / 2 Copy content Toggle raw display
ν13\nu^{13}== (4β19−22β18−10β17+24β16−4β15+18β14+34β13+⋯+16)/2 ( 4 \beta_{19} - 22 \beta_{18} - 10 \beta_{17} + 24 \beta_{16} - 4 \beta_{15} + 18 \beta_{14} + 34 \beta_{13} + \cdots + 16 ) / 2 Copy content Toggle raw display
ν14\nu^{14}== (−36β19+58β18+22β17−56β16+92β15−14β14+⋯+β1)/2 ( - 36 \beta_{19} + 58 \beta_{18} + 22 \beta_{17} - 56 \beta_{16} + 92 \beta_{15} - 14 \beta_{14} + \cdots + \beta_1 ) / 2 Copy content Toggle raw display
ν15\nu^{15}== (52β19+42β18−10β17−8β16−4β15−14β14−30β13+⋯−80)/2 ( 52 \beta_{19} + 42 \beta_{18} - 10 \beta_{17} - 8 \beta_{16} - 4 \beta_{15} - 14 \beta_{14} - 30 \beta_{13} + \cdots - 80 ) / 2 Copy content Toggle raw display
ν16\nu^{16}== (12β19−70β18−42β17+8β16+156β15+242β14+⋯+128)/2 ( 12 \beta_{19} - 70 \beta_{18} - 42 \beta_{17} + 8 \beta_{16} + 156 \beta_{15} + 242 \beta_{14} + \cdots + 128 ) / 2 Copy content Toggle raw display
ν17\nu^{17}== (−124β19+42β18+22β17−104β16+188β15−14β14+⋯−336)/2 ( - 124 \beta_{19} + 42 \beta_{18} + 22 \beta_{17} - 104 \beta_{16} + 188 \beta_{15} - 14 \beta_{14} + \cdots - 336 ) / 2 Copy content Toggle raw display
ν18\nu^{18}== (−132β19−38β18−170β17−88β16+220β15−206β14+⋯−160)/2 ( - 132 \beta_{19} - 38 \beta_{18} - 170 \beta_{17} - 88 \beta_{16} + 220 \beta_{15} - 206 \beta_{14} + \cdots - 160 ) / 2 Copy content Toggle raw display
ν19\nu^{19}== (−204β19−118β18+278β17+56β16+444β15−142β14+⋯−176)/2 ( - 204 \beta_{19} - 118 \beta_{18} + 278 \beta_{17} + 56 \beta_{16} + 444 \beta_{15} - 142 \beta_{14} + \cdots - 176 ) / 2 Copy content Toggle raw display

Display βi\beta_i in terms of νj\nu^j

Character values

We give the values of χ\chi on generators for (Z/968Z)×\left(\mathbb{Z}/968\mathbb{Z}\right)^\times.

nn 485485 727727 849849
χ(n)\chi(n) −1-1 11 11

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\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   ιm(ν)\iota_m(\nu) a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
485.1
−1.40720 + 0.140637i
−1.40720 − 0.140637i
−1.30820 + 0.537231i
−1.30820 − 0.537231i
−1.07012 + 0.924577i
−1.07012 − 0.924577i
−0.549610 + 1.30305i
−0.549610 − 1.30305i
−0.343983 + 1.37174i
−0.343983 − 1.37174i
0.324509 + 1.37648i
0.324509 − 1.37648i
0.651763 + 1.25507i
0.651763 − 1.25507i
0.926370 + 1.06857i
0.926370 − 1.06857i
1.37876 + 0.314658i
1.37876 − 0.314658i
1.39771 + 0.215430i
1.39771 − 0.215430i
−1.40720 − 0.140637i 2.55485i 1.96044 + 0.395809i 2.69541i 0.359306 − 3.59519i 3.94908 −2.70308 − 0.832694i −3.52726 0.379074 − 3.79299i
485.2 −1.40720 + 0.140637i − 2.55485i 1.96044 − 0.395809i − 2.69541i 0.359306 + 3.59519i 3.94908 −2.70308 + 0.832694i −3.52726 0.379074 + 3.79299i
485.3 −1.30820 − 0.537231i 1.28633i 1.42276 + 1.40561i 1.58193i 0.691057 − 1.68277i −1.86825 −1.10612 − 2.60317i 1.34535 0.849862 − 2.06948i
485.4 −1.30820 + 0.537231i − 1.28633i 1.42276 − 1.40561i − 1.58193i 0.691057 + 1.68277i −1.86825 −1.10612 + 2.60317i 1.34535 0.849862 + 2.06948i
485.5 −1.07012 − 0.924577i 0.321222i 0.290315 + 1.97882i − 1.28733i 0.296994 − 0.343746i −3.30669 1.51890 − 2.38599i 2.89682 −1.19023 + 1.37759i
485.6 −1.07012 + 0.924577i − 0.321222i 0.290315 − 1.97882i 1.28733i 0.296994 + 0.343746i −3.30669 1.51890 + 2.38599i 2.89682 −1.19023 − 1.37759i
485.7 −0.549610 − 1.30305i 0.612207i −1.39586 + 1.43233i − 1.46030i 0.797733 − 0.336475i 4.42813 2.63357 + 1.03164i 2.62520 −1.90283 + 0.802592i
485.8 −0.549610 + 1.30305i − 0.612207i −1.39586 − 1.43233i 1.46030i 0.797733 + 0.336475i 4.42813 2.63357 − 1.03164i 2.62520 −1.90283 − 0.802592i
485.9 −0.343983 − 1.37174i − 2.85679i −1.76335 + 0.943713i 2.60791i −3.91878 + 0.982689i 0.196362 1.90109 + 2.09424i −5.16127 3.57737 − 0.897076i
485.10 −0.343983 + 1.37174i 2.85679i −1.76335 − 0.943713i − 2.60791i −3.91878 − 0.982689i 0.196362 1.90109 − 2.09424i −5.16127 3.57737 + 0.897076i
485.11 0.324509 − 1.37648i 0.540427i −1.78939 − 0.893360i − 2.90090i 0.743887 + 0.175374i 2.60451 −1.81036 + 2.17315i 2.70794 −3.99302 − 0.941367i
485.12 0.324509 + 1.37648i − 0.540427i −1.78939 + 0.893360i 2.90090i 0.743887 − 0.175374i 2.60451 −1.81036 − 2.17315i 2.70794 −3.99302 + 0.941367i
485.13 0.651763 − 1.25507i 2.44793i −1.15041 − 1.63602i − 0.200474i 3.07232 + 1.59547i −2.34615 −2.80312 + 0.377551i −2.99235 −0.251609 − 0.130662i
485.14 0.651763 + 1.25507i − 2.44793i −1.15041 + 1.63602i 0.200474i 3.07232 − 1.59547i −2.34615 −2.80312 − 0.377551i −2.99235 −0.251609 + 0.130662i
485.15 0.926370 − 1.06857i − 2.75783i −0.283677 − 1.97978i − 2.90574i −2.94693 − 2.55477i 2.36352 −2.37832 − 1.53088i −4.60564 −3.10498 − 2.69179i
485.16 0.926370 + 1.06857i 2.75783i −0.283677 + 1.97978i 2.90574i −2.94693 + 2.55477i 2.36352 −2.37832 + 1.53088i −4.60564 −3.10498 + 2.69179i
485.17 1.37876 − 0.314658i 1.87996i 1.80198 − 0.867678i − 0.493106i 0.591545 + 2.59203i 0.174770 2.21148 − 1.76333i −0.534260 −0.155160 − 0.679877i
485.18 1.37876 + 0.314658i − 1.87996i 1.80198 + 0.867678i 0.493106i 0.591545 − 2.59203i 0.174770 2.21148 + 1.76333i −0.534260 −0.155160 + 0.679877i
485.19 1.39771 − 0.215430i − 0.868641i 1.90718 − 0.602216i 3.67418i −0.187131 − 1.21411i −1.19528 2.53595 − 1.25259i 2.24546 0.791527 + 5.13543i
485.20 1.39771 + 0.215430i 0.868641i 1.90718 + 0.602216i − 3.67418i −0.187131 + 1.21411i −1.19528 2.53595 + 1.25259i 2.24546 0.791527 − 5.13543i
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 485.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 968.2.c.h 20
4.b odd 2 1 3872.2.c.h 20
8.b even 2 1 inner 968.2.c.h 20
8.d odd 2 1 3872.2.c.h 20
11.b odd 2 1 968.2.c.i 20
11.c even 5 2 88.2.o.a ✓ 40
11.c even 5 2 968.2.o.j 40
11.d odd 10 2 968.2.o.d 40
11.d odd 10 2 968.2.o.i 40
33.h odd 10 2 792.2.br.b 40
44.c even 2 1 3872.2.c.i 20
44.h odd 10 2 352.2.w.a 40
88.b odd 2 1 968.2.c.i 20
88.g even 2 1 3872.2.c.i 20
88.l odd 10 2 352.2.w.a 40
88.o even 10 2 88.2.o.a ✓ 40
88.o even 10 2 968.2.o.j 40
88.p odd 10 2 968.2.o.d 40
88.p odd 10 2 968.2.o.i 40
264.t odd 10 2 792.2.br.b 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
88.2.o.a ✓ 40 11.c even 5 2
88.2.o.a ✓ 40 88.o even 10 2
352.2.w.a 40 44.h odd 10 2
352.2.w.a 40 88.l odd 10 2
792.2.br.b 40 33.h odd 10 2
792.2.br.b 40 264.t odd 10 2
968.2.c.h 20 1.a even 1 1 trivial
968.2.c.h 20 8.b even 2 1 inner
968.2.c.i 20 11.b odd 2 1
968.2.c.i 20 88.b odd 2 1
968.2.o.d 40 11.d odd 10 2
968.2.o.d 40 88.p odd 10 2
968.2.o.i 40 11.d odd 10 2
968.2.o.i 40 88.p odd 10 2
968.2.o.j 40 11.c even 5 2
968.2.o.j 40 88.o even 10 2
3872.2.c.h 20 4.b odd 2 1
3872.2.c.h 20 8.d odd 2 1
3872.2.c.i 20 44.c even 2 1
3872.2.c.i 20 88.g even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S2new(968,[χ])S_{2}^{\mathrm{new}}(968, [\chi]):

T320+35T318+503T316+3822T314+16493T312+40565T310+⋯+121 T_{3}^{20} + 35 T_{3}^{18} + 503 T_{3}^{16} + 3822 T_{3}^{14} + 16493 T_{3}^{12} + 40565 T_{3}^{10} + \cdots + 121 Copy content Toggle raw display
T520+51T518+1082T516+12427T514+84082T512+341655T510+⋯+4096 T_{5}^{20} + 51 T_{5}^{18} + 1082 T_{5}^{16} + 12427 T_{5}^{14} + 84082 T_{5}^{12} + 341655 T_{5}^{10} + \cdots + 4096 Copy content Toggle raw display
T710−5T79−22T78+111T77+176T76−775T75−701T74+⋯+64 T_{7}^{10} - 5 T_{7}^{9} - 22 T_{7}^{8} + 111 T_{7}^{7} + 176 T_{7}^{6} - 775 T_{7}^{5} - 701 T_{7}^{4} + \cdots + 64 Copy content Toggle raw display

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 T20−T18+⋯+1024 T^{20} - T^{18} + \cdots + 1024 Copy content Toggle raw display
33 T20+35T18+⋯+121 T^{20} + 35 T^{18} + \cdots + 121 Copy content Toggle raw display
55 T20+51T18+⋯+4096 T^{20} + 51 T^{18} + \cdots + 4096 Copy content Toggle raw display
77 (T10−5T9+⋯+64)2 (T^{10} - 5 T^{9} + \cdots + 64)^{2} Copy content Toggle raw display
1111 T20 T^{20} Copy content Toggle raw display
1313 T20+119T18+⋯+5308416 T^{20} + 119 T^{18} + \cdots + 5308416 Copy content Toggle raw display
1717 (T10−T9+⋯−34029)2 (T^{10} - T^{9} + \cdots - 34029)^{2} Copy content Toggle raw display
1919 T20+147T18+⋯+31036041 T^{20} + 147 T^{18} + \cdots + 31036041 Copy content Toggle raw display
2323 (T10+2T9+⋯−451584)2 (T^{10} + 2 T^{9} + \cdots - 451584)^{2} Copy content Toggle raw display
2929 T20+⋯+527896576 T^{20} + \cdots + 527896576 Copy content Toggle raw display
3131 (T10−T9+⋯−590144)2 (T^{10} - T^{9} + \cdots - 590144)^{2} Copy content Toggle raw display
3737 T20+⋯+478554034176 T^{20} + \cdots + 478554034176 Copy content Toggle raw display
4141 (T10+T9+⋯+685431)2 (T^{10} + T^{9} + \cdots + 685431)^{2} Copy content Toggle raw display
4343 T20+⋯+258242846976 T^{20} + \cdots + 258242846976 Copy content Toggle raw display
4747 (T10−T9+⋯+251136)2 (T^{10} - T^{9} + \cdots + 251136)^{2} Copy content Toggle raw display
5353 T20+⋯+4813029376 T^{20} + \cdots + 4813029376 Copy content Toggle raw display
5959 T20+⋯+91511695081 T^{20} + \cdots + 91511695081 Copy content Toggle raw display
6161 T20+⋯+47 ⁣⋯ ⁣96 T^{20} + \cdots + 47\!\cdots\!96 Copy content Toggle raw display
6767 T20+⋯+22416209899776 T^{20} + \cdots + 22416209899776 Copy content Toggle raw display
7171 (T10+17T9+⋯−2283264)2 (T^{10} + 17 T^{9} + \cdots - 2283264)^{2} Copy content Toggle raw display
7373 (T10−T9+⋯+4889699)2 (T^{10} - T^{9} + \cdots + 4889699)^{2} Copy content Toggle raw display
7979 (T10+29T9+⋯+36844544)2 (T^{10} + 29 T^{9} + \cdots + 36844544)^{2} Copy content Toggle raw display
8383 T20+⋯+17926799881 T^{20} + \cdots + 17926799881 Copy content Toggle raw display
8989 (T10+4T9+⋯−6007233744)2 (T^{10} + 4 T^{9} + \cdots - 6007233744)^{2} Copy content Toggle raw display
9797 (T10−5T9+⋯−140501)2 (T^{10} - 5 T^{9} + \cdots - 140501)^{2} Copy content Toggle raw display
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