[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2312.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(1\)
\(17\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 2T_{3}^{3} - 102T_{3}^{2} + 40T_{3} + 2056 \)
T3^4 - 2*T3^3 - 102*T3^2 + 40*T3 + 2056
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2312))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} - 2 T^{3} - 102 T^{2} + \cdots + 2056 \)
T^4 - 2*T^3 - 102*T^2 + 40*T + 2056
$5$
\( T^{4} + 8 T^{3} - 492 T^{2} + \cdots + 49664 \)
T^4 + 8*T^3 - 492*T^2 - 2528*T + 49664
$7$
\( T^{4} - 22 T^{3} - 450 T^{2} + \cdots + 53408 \)
T^4 - 22*T^3 - 450*T^2 + 7360*T + 53408
$11$
\( T^{4} + 70 T^{3} - 30 T^{2} + \cdots - 42648 \)
T^4 + 70*T^3 - 30*T^2 - 18456*T - 42648
$13$
\( T^{4} - 120 T^{3} + 396 T^{2} + \cdots - 4442400 \)
T^4 - 120*T^3 + 396*T^2 + 281296*T - 4442400
$17$
\( T^{4} \)
T^4
$19$
\( T^{4} + 44 T^{3} + \cdots + 102082944 \)
T^4 + 44*T^3 - 24600*T^2 - 880896*T + 102082944
$23$
\( T^{4} + 158 T^{3} + \cdots - 12352512 \)
T^4 + 158*T^3 - 40938*T^2 - 6132192*T - 12352512
$29$
\( T^{4} + 264 T^{3} + \cdots - 218365440 \)
T^4 + 264*T^3 - 37932*T^2 - 10480096*T - 218365440
$31$
\( T^{4} + 122 T^{3} + \cdots - 176821472 \)
T^4 + 122*T^3 - 39162*T^2 - 5959936*T - 176821472
$37$
\( T^{4} + 256 T^{3} + \cdots + 249018816 \)
T^4 + 256*T^3 - 26364*T^2 - 5652672*T + 249018816
$41$
\( T^{4} + 240 T^{3} + \cdots + 375609744 \)
T^4 + 240*T^3 - 76392*T^2 - 15525312*T + 375609744
$43$
\( T^{4} + 1100 T^{3} + \cdots + 3770813440 \)
T^4 + 1100*T^3 + 417336*T^2 + 66359744*T + 3770813440
$47$
\( T^{4} + 800 T^{3} + \cdots - 6901727232 \)
T^4 + 800*T^3 + 125904*T^2 - 30455808*T - 6901727232
$53$
\( T^{4} - 432 T^{3} + \cdots - 760197936 \)
T^4 - 432*T^3 - 43800*T^2 + 16561792*T - 760197936
$59$
\( T^{4} + 148 T^{3} + \cdots + 29013926912 \)
T^4 + 148*T^3 - 399624*T^2 - 16008256*T + 29013926912
$61$
\( T^{4} - 728 T^{3} + \cdots - 11277074752 \)
T^4 - 728*T^3 - 74220*T^2 + 104685632*T - 11277074752
$67$
\( T^{4} + 1032 T^{3} + \cdots - 17768263680 \)
T^4 + 1032*T^3 - 49776*T^2 - 173035648*T - 17768263680
$71$
\( T^{4} + 798 T^{3} + \cdots + 4791702528 \)
T^4 + 798*T^3 - 325122*T^2 - 152794720*T + 4791702528
$73$
\( T^{4} - 1544 T^{3} + \cdots - 13827804272 \)
T^4 - 1544*T^3 + 662712*T^2 - 32404640*T - 13827804272
$79$
\( T^{4} + 758 T^{3} + \cdots + 2551374208 \)
T^4 + 758*T^3 - 112314*T^2 - 20375776*T + 2551374208
$83$
\( T^{4} - 244 T^{3} + \cdots - 5249932288 \)
T^4 - 244*T^3 - 317832*T^2 + 111269440*T - 5249932288
$89$
\( T^{4} - 1440 T^{3} + \cdots - 46211953056 \)
T^4 - 1440*T^3 - 209556*T^2 + 486229744*T - 46211953056
$97$
\( T^{4} - 1344 T^{3} + \cdots - 1542436982448 \)
T^4 - 1344*T^3 - 1889976*T^2 + 3775191488*T - 1542436982448
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