[N,k,chi] = [912,6,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.1");
S:= CuspForms(chi, 6);
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
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} + 84T_{5}^{3} - 4731T_{5}^{2} - 267930T_{5} - 2835216 \)
T5^4 + 84*T5^3 - 4731*T5^2 - 267930*T5 - 2835216
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(912))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( (T - 9)^{4} \)
(T - 9)^4
$5$
\( T^{4} + 84 T^{3} - 4731 T^{2} + \cdots - 2835216 \)
T^4 + 84*T^3 - 4731*T^2 - 267930*T - 2835216
$7$
\( T^{4} + 54 T^{3} - 23183 T^{2} + \cdots - 11289056 \)
T^4 + 54*T^3 - 23183*T^2 + 983868*T - 11289056
$11$
\( T^{4} + 354 T^{3} + \cdots - 285160800 \)
T^4 + 354*T^3 - 175087*T^2 + 16518588*T - 285160800
$13$
\( T^{4} - 46 T^{3} + \cdots - 24059151936 \)
T^4 - 46*T^3 - 1028612*T^2 + 314698968*T - 24059151936
$17$
\( T^{4} - 2046 T^{3} + \cdots - 340390896708 \)
T^4 - 2046*T^3 + 358445*T^2 + 931872408*T - 340390896708
$19$
\( (T + 361)^{4} \)
(T + 361)^4
$23$
\( T^{4} + 846 T^{3} + \cdots + 30031102634496 \)
T^4 + 846*T^3 - 11576800*T^2 - 2991237024*T + 30031102634496
$29$
\( T^{4} + \cdots - 312735730784112 \)
T^4 + 7152*T^3 - 14150760*T^2 - 183428364096*T - 312735730784112
$31$
\( T^{4} + 238 T^{3} + \cdots + 44788434085728 \)
T^4 + 238*T^3 - 53770796*T^2 - 108499861272*T + 44788434085728
$37$
\( T^{4} + \cdots - 371485366814720 \)
T^4 + 10326*T^3 - 18768224*T^2 - 347944076928*T - 371485366814720
$41$
\( T^{4} + 28200 T^{3} + \cdots - 57\!\cdots\!00 \)
T^4 + 28200*T^3 - 206108596*T^2 - 10290223357440*T - 57919674933331200
$43$
\( T^{4} - 18590 T^{3} + \cdots - 47\!\cdots\!60 \)
T^4 - 18590*T^3 - 404911079*T^2 + 9704435748648*T - 47476018614645360
$47$
\( T^{4} - 18684 T^{3} + \cdots - 18\!\cdots\!68 \)
T^4 - 18684*T^3 - 173727979*T^2 + 1601484184338*T - 1899759337935168
$53$
\( T^{4} + 42720 T^{3} + \cdots - 33\!\cdots\!96 \)
T^4 + 42720*T^3 - 441533656*T^2 - 35815557380928*T - 337103569253461296
$59$
\( T^{4} - 68256 T^{3} + \cdots + 13\!\cdots\!00 \)
T^4 - 68256*T^3 + 1211549744*T^2 - 5942178353280*T + 1392045732057600
$61$
\( T^{4} + 67654 T^{3} + \cdots - 40\!\cdots\!60 \)
T^4 + 67654*T^3 + 799705845*T^2 - 23454675152684*T - 401402040225842060
$67$
\( T^{4} - 81836 T^{3} + \cdots - 26\!\cdots\!12 \)
T^4 - 81836*T^3 - 941631104*T^2 + 180956867546496*T - 2672958689497331712
$71$
\( T^{4} - 62112 T^{3} + \cdots + 18\!\cdots\!00 \)
T^4 - 62112*T^3 - 1728324784*T^2 + 19267170724608*T + 188869739983257600
$73$
\( T^{4} + 81966 T^{3} + \cdots + 10\!\cdots\!00 \)
T^4 + 81966*T^3 - 2979416987*T^2 - 240273312408432*T + 1056317338825509100
$79$
\( T^{4} + 8766 T^{3} + \cdots + 56\!\cdots\!04 \)
T^4 + 8766*T^3 - 10545715400*T^2 - 219537079098624*T + 5684757380088680704
$83$
\( T^{4} - 55080 T^{3} + \cdots - 82\!\cdots\!96 \)
T^4 - 55080*T^3 - 5691347056*T^2 - 125098379845632*T - 829862467906768896
$89$
\( T^{4} + 197520 T^{3} + \cdots + 58\!\cdots\!16 \)
T^4 + 197520*T^3 + 4448908376*T^2 - 482644237207872*T + 5897926082768566416
$97$
\( T^{4} + 184228 T^{3} + \cdots + 22\!\cdots\!68 \)
T^4 + 184228*T^3 - 6539356704*T^2 - 1764174620332688*T + 2276256481952633968
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