[N,k,chi] = [1110,4,Mod(1,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, 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("1110.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(5\)
\(1\)
\(37\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{4} + 23T_{7}^{3} - 557T_{7}^{2} - 6963T_{7} - 16680 \)
T7^4 + 23*T7^3 - 557*T7^2 - 6963*T7 - 16680
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1110))\).
$p$
$F_p(T)$
$2$
\( (T - 2)^{4} \)
(T - 2)^4
$3$
\( (T - 3)^{4} \)
(T - 3)^4
$5$
\( (T + 5)^{4} \)
(T + 5)^4
$7$
\( T^{4} + 23 T^{3} - 557 T^{2} + \cdots - 16680 \)
T^4 + 23*T^3 - 557*T^2 - 6963*T - 16680
$11$
\( T^{4} + 6 T^{3} - 2854 T^{2} + \cdots - 299716 \)
T^4 + 6*T^3 - 2854*T^2 - 59477*T - 299716
$13$
\( T^{4} + 59 T^{3} - 3255 T^{2} + \cdots + 1420990 \)
T^4 + 59*T^3 - 3255*T^2 - 168019*T + 1420990
$17$
\( T^{4} + 172 T^{3} - 2382 T^{2} + \cdots + 627862 \)
T^4 + 172*T^3 - 2382*T^2 - 987941*T + 627862
$19$
\( T^{4} + 256 T^{3} + \cdots - 51511592 \)
T^4 + 256*T^3 + 13586*T^2 - 709883*T - 51511592
$23$
\( T^{4} + 103 T^{3} + \cdots - 141260816 \)
T^4 + 103*T^3 - 24325*T^2 - 3875963*T - 141260816
$29$
\( T^{4} + 345 T^{3} + \cdots + 50882500 \)
T^4 + 345*T^3 + 5275*T^2 - 2092500*T + 50882500
$31$
\( T^{4} + 686 T^{3} + \cdots + 234681832 \)
T^4 + 686*T^3 + 157343*T^2 + 13139966*T + 234681832
$37$
\( (T - 37)^{4} \)
(T - 37)^4
$41$
\( T^{4} + 672 T^{3} + \cdots - 2823967280 \)
T^4 + 672*T^3 + 101773*T^2 - 12355458*T - 2823967280
$43$
\( T^{4} + 421 T^{3} + \cdots - 351189408 \)
T^4 + 421*T^3 + 15445*T^2 - 7903140*T - 351189408
$47$
\( T^{4} + 344 T^{3} + \cdots + 663296928 \)
T^4 + 344*T^3 - 92585*T^2 - 14146188*T + 663296928
$53$
\( T^{4} - 63 T^{3} + \cdots + 16289516160 \)
T^4 - 63*T^3 - 260066*T^2 + 9930576*T + 16289516160
$59$
\( T^{4} - 121 T^{3} + \cdots + 59111981960 \)
T^4 - 121*T^3 - 561431*T^2 - 7770834*T + 59111981960
$61$
\( T^{4} + 390 T^{3} + \cdots - 39681273100 \)
T^4 + 390*T^3 - 537739*T^2 - 320311852*T - 39681273100
$67$
\( T^{4} + 845 T^{3} + \cdots - 6416221016 \)
T^4 + 845*T^3 - 95929*T^2 - 97104214*T - 6416221016
$71$
\( T^{4} + 53 T^{3} + \cdots + 593103510304 \)
T^4 + 53*T^3 - 1595209*T^2 - 64501054*T + 593103510304
$73$
\( T^{4} - 516 T^{3} + \cdots + 13095941550 \)
T^4 - 516*T^3 - 606542*T^2 + 13120497*T + 13095941550
$79$
\( T^{4} + 235 T^{3} + \cdots + 382378425184 \)
T^4 + 235*T^3 - 1818571*T^2 - 398600132*T + 382378425184
$83$
\( T^{4} + 1360 T^{3} + \cdots + 272148028388 \)
T^4 + 1360*T^3 - 616688*T^2 - 695342319*T + 272148028388
$89$
\( T^{4} + 2529 T^{3} + \cdots - 546655237958 \)
T^4 + 2529*T^3 + 445501*T^2 - 2000223225*T - 546655237958
$97$
\( T^{4} + 3438 T^{3} + \cdots - 505578013232 \)
T^4 + 3438*T^3 + 3144235*T^2 + 49692906*T - 505578013232
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