[N,k,chi] = [6,26,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 26);
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
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
\(2\)
\(1\)
\(3\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 292754850 \)
T5 + 292754850
acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(6))\).
$p$
$F_p(T)$
$2$
\( T + 4096 \)
T + 4096
$3$
\( T + 531441 \)
T + 531441
$5$
\( T + 292754850 \)
T + 292754850
$7$
\( T - 3580644032 \)
T - 3580644032
$11$
\( T - 15111573238212 \)
T - 15111573238212
$13$
\( T - 1221071681246 \)
T - 1221071681246
$17$
\( T - 2518250853863682 \)
T - 2518250853863682
$19$
\( T + 7992693407413060 \)
T + 7992693407413060
$23$
\( T + 99\!\cdots\!24 \)
T + 99645642629247624
$29$
\( T + 20\!\cdots\!90 \)
T + 2080672742244316890
$31$
\( T + 49\!\cdots\!08 \)
T + 4937672075835729208
$37$
\( T - 19\!\cdots\!82 \)
T - 19829154107621718182
$41$
\( T - 22\!\cdots\!42 \)
T - 224696060863159376442
$43$
\( T + 72\!\cdots\!84 \)
T + 72221008334482349884
$47$
\( T - 18\!\cdots\!92 \)
T - 189872435947262116992
$53$
\( T + 26\!\cdots\!74 \)
T + 2645676034335389555874
$59$
\( T + 16\!\cdots\!40 \)
T + 16454608826354674865340
$61$
\( T + 35\!\cdots\!38 \)
T + 35546954389065591688738
$67$
\( T - 10\!\cdots\!92 \)
T - 106703750402023286661692
$71$
\( T - 73\!\cdots\!12 \)
T - 73672004836753334994312
$73$
\( T + 26\!\cdots\!74 \)
T + 262402855870448192600374
$79$
\( T + 10\!\cdots\!40 \)
T + 1002642123108883497568840
$83$
\( T - 15\!\cdots\!96 \)
T - 1558588706101147601425596
$89$
\( T - 21\!\cdots\!90 \)
T - 2181670205644666928498490
$97$
\( T + 44\!\cdots\!58 \)
T + 440165308375605500117758
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