[N,k,chi] = [64,20,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 960\sqrt{1453}\).
We also show the integral \(q\)-expansion of the trace form .
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.
Refresh table
\( p \)
Sign
\(2\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 27912T_{3} - 1144314864 \)
T3^2 + 27912*T3 - 1144314864
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 27912 T - 1144314864 \)
T^2 + 27912*T - 1144314864
$5$
\( T^{2} + 1226620 T - 2216319016700 \)
T^2 + 1226620*T - 2216319016700
$7$
\( T^{2} + 88510512 T - 11\!\cdots\!64 \)
T^2 + 88510512*T - 11668133149654464
$11$
\( T^{2} + 7163787608 T - 54\!\cdots\!84 \)
T^2 + 7163787608*T - 54040584096044956784
$13$
\( T^{2} - 10126923604 T + 18\!\cdots\!04 \)
T^2 - 10126923604*T + 18762236610718207204
$17$
\( T^{2} + 72045078940 T - 40\!\cdots\!00 \)
T^2 + 72045078940*T - 401263031904452955875900
$19$
\( T^{2} + 3120480472232 T + 15\!\cdots\!56 \)
T^2 + 3120480472232*T + 1519506585866193671994256
$23$
\( T^{2} - 14759207090288 T + 89\!\cdots\!36 \)
T^2 - 14759207090288*T + 8978817310810979023260736
$29$
\( T^{2} - 30249539245044 T - 83\!\cdots\!16 \)
T^2 - 30249539245044*T - 839314375233113444628068316
$31$
\( T^{2} - 123389562777920 T - 16\!\cdots\!00 \)
T^2 - 123389562777920*T - 16190442440617846912814259200
$37$
\( T^{2} + \cdots + 10\!\cdots\!44 \)
T^2 + 2015393170174524*T + 1002811683993230747214907629444
$41$
\( T^{2} + \cdots - 13\!\cdots\!16 \)
T^2 - 2540784959504244*T - 1383985313593027027027800452316
$43$
\( T^{2} + \cdots + 75\!\cdots\!24 \)
T^2 + 5633655093389464*T + 7572930713027550855793070548624
$47$
\( T^{2} + \cdots + 12\!\cdots\!24 \)
T^2 - 21948339587130336*T + 120173475308689433909209933857024
$53$
\( T^{2} + \cdots - 85\!\cdots\!56 \)
T^2 - 9418125066904676*T - 857690623991584125962401383312956
$59$
\( T^{2} + \cdots + 66\!\cdots\!44 \)
T^2 - 98542449590407624*T + 660177372717092343192043681168144
$61$
\( T^{2} + \cdots - 15\!\cdots\!00 \)
T^2 + 10292145377839820*T - 15503627981825374659589316865547100
$67$
\( T^{2} + \cdots - 54\!\cdots\!96 \)
T^2 - 75753628003984504*T - 54599323301947677756480464364851696
$71$
\( T^{2} + \cdots - 21\!\cdots\!56 \)
T^2 + 17407052566713776*T - 21700241760991919332574106473310656
$73$
\( T^{2} + \cdots + 29\!\cdots\!56 \)
T^2 + 857508255059832268*T + 29843890690998648214115366394517156
$79$
\( T^{2} + \cdots - 91\!\cdots\!04 \)
T^2 - 226291921444855072*T - 91511177663647793432254566145781504
$83$
\( T^{2} + \cdots + 14\!\cdots\!76 \)
T^2 - 767515701460985048*T + 142559847240019285280425667078655376
$89$
\( T^{2} + \cdots + 92\!\cdots\!76 \)
T^2 - 6092545894435174548*T + 9212176762332249419592269581970130276
$97$
\( T^{2} + \cdots - 45\!\cdots\!56 \)
T^2 - 1548148249522347076*T - 45772170390785845952226048541312959356
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