[N,k,chi] = [31,4,Mod(1,31)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(31, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("31.1");
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
\(31\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} - 3T_{2}^{4} - 30T_{2}^{3} + 79T_{2}^{2} + 167T_{2} - 386 \)
T2^5 - 3*T2^4 - 30*T2^3 + 79*T2^2 + 167*T2 - 386
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(31))\).
$p$
$F_p(T)$
$2$
\( T^{5} - 3 T^{4} - 30 T^{3} + 79 T^{2} + \cdots - 386 \)
T^5 - 3*T^4 - 30*T^3 + 79*T^2 + 167*T - 386
$3$
\( T^{5} - 4 T^{4} - 74 T^{3} + 188 T^{2} + \cdots + 32 \)
T^5 - 4*T^4 - 74*T^3 + 188*T^2 + 856*T + 32
$5$
\( T^{5} - 15 T^{4} - 433 T^{3} + \cdots - 520516 \)
T^5 - 15*T^4 - 433*T^3 + 6375*T^2 + 35100*T - 520516
$7$
\( T^{5} - 9 T^{4} - 429 T^{3} + \cdots + 47236 \)
T^5 - 9*T^4 - 429*T^3 - 871*T^2 + 14520*T + 47236
$11$
\( T^{5} - 88 T^{4} - 562 T^{3} + \cdots - 76793648 \)
T^5 - 88*T^4 - 562*T^3 + 176124*T^2 - 1159400*T - 76793648
$13$
\( T^{5} + 28 T^{4} - 3850 T^{3} + \cdots + 85935616 \)
T^5 + 28*T^4 - 3850*T^3 - 99836*T^2 + 3363368*T + 85935616
$17$
\( T^{5} - 138 T^{4} + \cdots + 845793728 \)
T^5 - 138*T^4 - 5744*T^3 + 1416680*T^2 - 62408144*T + 845793728
$19$
\( T^{5} + 43 T^{4} + \cdots - 885299824 \)
T^5 + 43*T^4 - 20013*T^3 - 513799*T^2 + 84833096*T - 885299824
$23$
\( T^{5} - 206 T^{4} + \cdots - 1477525504 \)
T^5 - 206*T^4 - 4268*T^3 + 1612992*T^2 + 31264256*T - 1477525504
$29$
\( T^{5} - 474 T^{4} + \cdots + 6492808496 \)
T^5 - 474*T^4 + 70238*T^3 - 2819688*T^2 - 106998096*T + 6492808496
$31$
\( (T + 31)^{5} \)
(T + 31)^5
$37$
\( T^{5} + 508 T^{4} + \cdots - 315180705232 \)
T^5 + 508*T^4 - 25650*T^3 - 45066092*T^2 - 7010150696*T - 315180705232
$41$
\( T^{5} - 473 T^{4} + \cdots + 19192433688 \)
T^5 - 473*T^4 - 132137*T^3 + 88408661*T^2 - 10289561412*T + 19192433688
$43$
\( T^{5} + 82 T^{4} + \cdots - 154176970896 \)
T^5 + 82*T^4 - 232370*T^3 - 20709784*T^2 + 4684410240*T - 154176970896
$47$
\( T^{5} + 644 T^{4} + \cdots + 197408306432 \)
T^5 + 644*T^4 + 35236*T^3 - 32733376*T^2 - 3204167808*T + 197408306432
$53$
\( T^{5} - 374 T^{4} + \cdots + 79406336128 \)
T^5 - 374*T^4 - 168138*T^3 + 51574928*T^2 + 4303685312*T + 79406336128
$59$
\( T^{5} + 541 T^{4} + \cdots + 19804492743336 \)
T^5 + 541*T^4 - 489537*T^3 - 253089337*T^2 + 35770388652*T + 19804492743336
$61$
\( T^{5} - 440 T^{4} + \cdots + 922927740352 \)
T^5 - 440*T^4 - 322674*T^3 - 19295188*T^2 + 8535138216*T + 922927740352
$67$
\( T^{5} + 1884 T^{4} + \cdots - 22262005628928 \)
T^5 + 1884*T^4 + 946944*T^3 - 65348608*T^2 - 137973989376*T - 22262005628928
$71$
\( T^{5} - 491 T^{4} + \cdots - 69573929276736 \)
T^5 - 491*T^4 - 1083549*T^3 + 466152431*T^2 + 241993512960*T - 69573929276736
$73$
\( T^{5} - 302 T^{4} + \cdots - 1852644259168 \)
T^5 - 302*T^4 - 630904*T^3 + 262079248*T^2 - 17267778608*T - 1852644259168
$79$
\( T^{5} + 1244 T^{4} + \cdots - 59985571648 \)
T^5 + 1244*T^4 - 778144*T^3 - 963316120*T^2 - 63376557280*T - 59985571648
$83$
\( T^{5} - 1544 T^{4} + \cdots + 657431598704 \)
T^5 - 1544*T^4 + 521158*T^3 + 182720820*T^2 - 94455176136*T + 657431598704
$89$
\( T^{5} - 3056 T^{4} + \cdots + 68090734165536 \)
T^5 - 3056*T^4 + 2201156*T^3 + 788987256*T^2 - 1002344499360*T + 68090734165536
$97$
\( T^{5} - 583 T^{4} + \cdots - 31148274036888 \)
T^5 - 583*T^4 - 2505609*T^3 + 1000257787*T^2 + 1103001039468*T - 31148274036888
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