[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 2);
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
\(3\)
\(1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{8} - 4T_{2}^{7} - 2T_{2}^{6} + 20T_{2}^{5} - 4T_{2}^{4} - 30T_{2}^{3} + 7T_{2}^{2} + 12T_{2} + 1 \)
T2^8 - 4*T2^7 - 2*T2^6 + 20*T2^5 - 4*T2^4 - 30*T2^3 + 7*T2^2 + 12*T2 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1875))\).
$p$
$F_p(T)$
$2$
\( T^{8} - 4 T^{7} - 2 T^{6} + 20 T^{5} + \cdots + 1 \)
T^8 - 4*T^7 - 2*T^6 + 20*T^5 - 4*T^4 - 30*T^3 + 7*T^2 + 12*T + 1
$3$
\( (T + 1)^{8} \)
(T + 1)^8
$5$
\( T^{8} \)
T^8
$7$
\( T^{8} - 8 T^{7} + 4 T^{6} + 108 T^{5} + \cdots + 505 \)
T^8 - 8*T^7 + 4*T^6 + 108*T^5 - 254*T^4 - 160*T^3 + 1145*T^2 - 1340*T + 505
$11$
\( T^{8} - 2 T^{7} - 43 T^{6} + \cdots + 5281 \)
T^8 - 2*T^7 - 43*T^6 + 90*T^5 + 556*T^4 - 1010*T^3 - 2842*T^2 + 3274*T + 5281
$13$
\( T^{8} - 16 T^{7} + 73 T^{6} + \cdots + 281 \)
T^8 - 16*T^7 + 73*T^6 - 594*T^4 + 600*T^3 + 1032*T^2 - 1472*T + 281
$17$
\( T^{8} - 16 T^{7} + 42 T^{6} + \cdots - 7339 \)
T^8 - 16*T^7 + 42*T^6 + 442*T^5 - 2220*T^4 - 622*T^3 + 12407*T^2 - 2654*T - 7339
$19$
\( T^{8} + 14 T^{7} + 11 T^{6} + \cdots + 2525 \)
T^8 + 14*T^7 + 11*T^6 - 516*T^5 - 1599*T^4 + 2180*T^3 + 5715*T^2 - 8050*T + 2525
$23$
\( T^{8} - 14 T^{7} + 11 T^{6} + \cdots - 2095 \)
T^8 - 14*T^7 + 11*T^6 + 486*T^5 - 1484*T^4 - 1750*T^3 + 7950*T^2 - 2500*T - 2095
$29$
\( T^{8} - 2 T^{7} - 106 T^{6} + \cdots - 395 \)
T^8 - 2*T^7 - 106*T^6 + 162*T^5 + 2956*T^4 - 2330*T^3 - 16095*T^2 + 11650*T - 395
$31$
\( T^{8} + 22 T^{7} + 169 T^{6} + \cdots + 125 \)
T^8 + 22*T^7 + 169*T^6 + 548*T^5 + 586*T^4 - 390*T^3 - 700*T^2 + 125
$37$
\( T^{8} - 28 T^{7} + 204 T^{6} + \cdots + 93025 \)
T^8 - 28*T^7 + 204*T^6 + 428*T^5 - 6794*T^4 - 7000*T^3 + 65265*T^2 + 152500*T + 93025
$41$
\( T^{8} - 8 T^{7} - 56 T^{6} + \cdots + 4705 \)
T^8 - 8*T^7 - 56*T^6 + 428*T^5 + 166*T^4 - 5680*T^3 + 13920*T^2 - 13460*T + 4705
$43$
\( T^{8} - 20 T^{7} + 6 T^{6} + \cdots + 22961 \)
T^8 - 20*T^7 + 6*T^6 + 1760*T^5 - 6949*T^4 - 26000*T^3 + 164886*T^2 - 215140*T + 22961
$47$
\( T^{8} - 10 T^{7} - 186 T^{6} + \cdots - 6057019 \)
T^8 - 10*T^7 - 186*T^6 + 1980*T^5 + 9856*T^4 - 130810*T^3 - 36051*T^2 + 2873300*T - 6057019
$53$
\( T^{8} - 44 T^{7} + 746 T^{6} + \cdots - 200995 \)
T^8 - 44*T^7 + 746*T^6 - 5914*T^5 + 18836*T^4 + 18390*T^3 - 262425*T^2 + 513930*T - 200995
$59$
\( T^{8} - 14 T^{7} - 29 T^{6} + \cdots - 3595 \)
T^8 - 14*T^7 - 29*T^6 + 886*T^5 - 1689*T^4 - 8970*T^3 + 28695*T^2 - 15080*T - 3595
$61$
\( T^{8} + 20 T^{7} - 136 T^{6} + \cdots + 16604261 \)
T^8 + 20*T^7 - 136*T^6 - 5500*T^5 - 27214*T^4 + 256380*T^3 + 3212144*T^2 + 12349420*T + 16604261
$67$
\( T^{8} - 16 T^{7} - 138 T^{6} + \cdots - 3739 \)
T^8 - 16*T^7 - 138*T^6 + 3652*T^5 - 20225*T^4 + 34668*T^3 + 9362*T^2 - 44284*T - 3739
$71$
\( T^{8} - 16 T^{7} - 78 T^{6} + \cdots - 159779 \)
T^8 - 16*T^7 - 78*T^6 + 2162*T^5 - 5420*T^4 - 41822*T^3 + 138507*T^2 + 142086*T - 159779
$73$
\( T^{8} - 24 T^{7} - 34 T^{6} + \cdots - 870295 \)
T^8 - 24*T^7 - 34*T^6 + 5216*T^5 - 45829*T^4 + 66880*T^3 + 630150*T^2 - 1796760*T - 870295
$79$
\( T^{8} + 30 T^{7} + 145 T^{6} + \cdots - 1984975 \)
T^8 + 30*T^7 + 145*T^6 - 2680*T^5 - 19590*T^4 + 74350*T^3 + 499600*T^2 - 851400*T - 1984975
$83$
\( T^{8} - 12 T^{7} - 188 T^{6} + \cdots + 48541 \)
T^8 - 12*T^7 - 188*T^6 + 2560*T^5 + 4186*T^4 - 127820*T^3 + 412308*T^2 - 302696*T + 48541
$89$
\( T^{8} - 16 T^{7} - 39 T^{6} + 1454 T^{5} + \cdots + 5 \)
T^8 - 16*T^7 - 39*T^6 + 1454*T^5 - 5504*T^4 + 6620*T^3 - 2830*T^2 + 370*T + 5
$97$
\( T^{8} - 16 T^{7} - 108 T^{6} + \cdots - 14719 \)
T^8 - 16*T^7 - 108*T^6 + 2432*T^5 - 1370*T^4 - 80272*T^3 + 138132*T^2 + 432096*T - 14719
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