[N,k,chi] = [452,2,Mod(1,452)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(452, 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("452.1");
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
\(2\)
\(-1\)
\(113\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{7} - 3T_{3}^{6} - 12T_{3}^{5} + 33T_{3}^{4} + 40T_{3}^{3} - 98T_{3}^{2} - 16T_{3} + 58 \)
T3^7 - 3*T3^6 - 12*T3^5 + 33*T3^4 + 40*T3^3 - 98*T3^2 - 16*T3 + 58
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(452))\).
$p$
$F_p(T)$
$2$
\( T^{7} \)
T^7
$3$
\( T^{7} - 3 T^{6} - 12 T^{5} + 33 T^{4} + \cdots + 58 \)
T^7 - 3*T^6 - 12*T^5 + 33*T^4 + 40*T^3 - 98*T^2 - 16*T + 58
$5$
\( T^{7} - 3 T^{6} - 21 T^{5} + 67 T^{4} + \cdots + 240 \)
T^7 - 3*T^6 - 21*T^5 + 67*T^4 + 76*T^3 - 272*T^2 - 32*T + 240
$7$
\( T^{7} - 29 T^{5} + 5 T^{4} + 232 T^{3} + \cdots + 320 \)
T^7 - 29*T^5 + 5*T^4 + 232*T^3 - 96*T^2 - 512*T + 320
$11$
\( T^{7} - 4 T^{6} - 49 T^{5} + \cdots + 4704 \)
T^7 - 4*T^6 - 49*T^5 + 203*T^4 + 444*T^3 - 1856*T^2 - 1120*T + 4704
$13$
\( T^{7} - 16 T^{6} + 69 T^{5} + \cdots - 892 \)
T^7 - 16*T^6 + 69*T^5 + 85*T^4 - 1124*T^3 + 1620*T^2 + 852*T - 892
$17$
\( T^{7} - 14 T^{6} + 55 T^{5} + 5 T^{4} + \cdots - 48 \)
T^7 - 14*T^6 + 55*T^5 + 5*T^4 - 328*T^3 + 232*T^2 + 176*T - 48
$19$
\( T^{7} - 8 T^{6} - 31 T^{5} + \cdots + 3398 \)
T^7 - 8*T^6 - 31*T^5 + 305*T^4 + 108*T^3 - 2748*T^2 + 1058*T + 3398
$23$
\( T^{7} - 59 T^{5} + 3 T^{4} + \cdots - 2430 \)
T^7 - 59*T^5 + 3*T^4 + 972*T^3 + 108*T^2 - 4374*T - 2430
$29$
\( T^{7} - 5 T^{6} - 114 T^{5} + 381 T^{4} + \cdots - 48 \)
T^7 - 5*T^6 - 114*T^5 + 381*T^4 + 3572*T^3 - 5104*T^2 - 9328*T - 48
$31$
\( T^{7} + T^{6} - 104 T^{5} - 115 T^{4} + \cdots + 3104 \)
T^7 + T^6 - 104*T^5 - 115*T^4 + 2724*T^3 + 4320*T^2 - 9120*T + 3104
$37$
\( T^{7} - 6 T^{6} - 103 T^{5} + \cdots - 18000 \)
T^7 - 6*T^6 - 103*T^5 + 679*T^4 + 1700*T^3 - 16880*T^2 + 32256*T - 18000
$41$
\( T^{7} - T^{6} - 152 T^{5} + 221 T^{4} + \cdots + 1380 \)
T^7 - T^6 - 152*T^5 + 221*T^4 + 4728*T^3 - 7952*T^2 - 9088*T + 1380
$43$
\( T^{7} - 8 T^{6} - 35 T^{5} + 179 T^{4} + \cdots + 2 \)
T^7 - 8*T^6 - 35*T^5 + 179*T^4 + 180*T^3 - 18*T + 2
$47$
\( T^{7} + 15 T^{6} - 194 T^{5} + \cdots - 1796634 \)
T^7 + 15*T^6 - 194*T^5 - 3165*T^4 + 8408*T^3 + 173658*T^2 + 14112*T - 1796634
$53$
\( T^{7} + T^{6} - 140 T^{5} + \cdots + 116868 \)
T^7 + T^6 - 140*T^5 + 197*T^4 + 4792*T^3 - 11400*T^2 - 42400*T + 116868
$59$
\( T^{7} + 15 T^{6} - 82 T^{5} + \cdots + 21162 \)
T^7 + 15*T^6 - 82*T^5 - 2371*T^4 - 11064*T^3 - 590*T^2 + 57212*T + 21162
$61$
\( T^{7} - 15 T^{6} - 8 T^{5} + \cdots + 69760 \)
T^7 - 15*T^6 - 8*T^5 + 853*T^4 - 1448*T^3 - 13984*T^2 + 21568*T + 69760
$67$
\( T^{7} + T^{6} - 224 T^{5} + \cdots + 157754 \)
T^7 + T^6 - 224*T^5 - 31*T^4 + 13368*T^3 - 9114*T^2 - 110364*T + 157754
$71$
\( T^{7} + 24 T^{6} - 68 T^{5} + \cdots + 1451376 \)
T^7 + 24*T^6 - 68*T^5 - 4804*T^4 - 18430*T^3 + 205932*T^2 + 1351856*T + 1451376
$73$
\( T^{7} - 41 T^{6} + 458 T^{5} + \cdots - 185392 \)
T^7 - 41*T^6 + 458*T^5 + 2153*T^4 - 77760*T^3 + 528600*T^2 - 1127776*T - 185392
$79$
\( T^{7} + 21 T^{6} - 78 T^{5} + \cdots - 2349362 \)
T^7 + 21*T^6 - 78*T^5 - 3841*T^4 - 10768*T^3 + 151374*T^2 + 394608*T - 2349362
$83$
\( T^{7} + 14 T^{6} - 43 T^{5} + \cdots + 13632 \)
T^7 + 14*T^6 - 43*T^5 - 887*T^4 - 2376*T^3 + 2368*T^2 + 15232*T + 13632
$89$
\( T^{7} + 40 T^{6} + 463 T^{5} + \cdots - 1465104 \)
T^7 + 40*T^6 + 463*T^5 - 1153*T^4 - 63536*T^3 - 489752*T^2 - 1475504*T - 1465104
$97$
\( T^{7} - 24 T^{6} - 73 T^{5} + \cdots - 1300608 \)
T^7 - 24*T^6 - 73*T^5 + 6891*T^4 - 73312*T^3 + 274208*T^2 - 43968*T - 1300608
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