[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4030.1");
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
\(2\)
\(-1\)
\(5\)
\(1\)
\(13\)
\(-1\)
\(31\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{9} - 3T_{3}^{8} - 16T_{3}^{7} + 48T_{3}^{6} + 66T_{3}^{5} - 202T_{3}^{4} - 75T_{3}^{3} + 210T_{3}^{2} + 68T_{3} - 16 \)
T3^9 - 3*T3^8 - 16*T3^7 + 48*T3^6 + 66*T3^5 - 202*T3^4 - 75*T3^3 + 210*T3^2 + 68*T3 - 16
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{9} \)
(T - 1)^9
$3$
\( T^{9} - 3 T^{8} - 16 T^{7} + 48 T^{6} + \cdots - 16 \)
T^9 - 3*T^8 - 16*T^7 + 48*T^6 + 66*T^5 - 202*T^4 - 75*T^3 + 210*T^2 + 68*T - 16
$5$
\( (T + 1)^{9} \)
(T + 1)^9
$7$
\( T^{9} - 3 T^{8} - 31 T^{7} + 94 T^{6} + \cdots + 8 \)
T^9 - 3*T^8 - 31*T^7 + 94*T^6 + 186*T^5 - 797*T^4 + 620*T^3 + 30*T^2 - 67*T + 8
$11$
\( T^{9} - 6 T^{8} - 31 T^{7} + \cdots + 1944 \)
T^9 - 6*T^8 - 31*T^7 + 202*T^6 + 234*T^5 - 2124*T^4 + 537*T^3 + 6972*T^2 - 7560*T + 1944
$13$
\( (T - 1)^{9} \)
(T - 1)^9
$17$
\( T^{9} - 3 T^{8} - 102 T^{7} + \cdots + 231444 \)
T^9 - 3*T^8 - 102*T^7 + 155*T^6 + 3582*T^5 - 882*T^4 - 47745*T^3 - 28374*T^2 + 196893*T + 231444
$19$
\( T^{9} - 6 T^{8} - 67 T^{7} + \cdots - 4424 \)
T^9 - 6*T^8 - 67*T^7 + 456*T^6 + 252*T^5 - 6107*T^4 + 9846*T^3 + 4317*T^2 - 11017*T - 4424
$23$
\( T^{9} - 14 T^{8} + 16 T^{7} + \cdots + 16794 \)
T^9 - 14*T^8 + 16*T^7 + 461*T^6 - 1419*T^5 - 3420*T^4 + 14439*T^3 - 366*T^2 - 27549*T + 16794
$29$
\( T^{9} - 17 T^{8} + 38 T^{7} + \cdots - 52488 \)
T^9 - 17*T^8 + 38*T^7 + 541*T^6 - 2076*T^5 - 4554*T^4 + 19035*T^3 + 21384*T^2 - 50301*T - 52488
$31$
\( (T - 1)^{9} \)
(T - 1)^9
$37$
\( T^{9} + 3 T^{8} - 76 T^{7} + \cdots - 24074 \)
T^9 + 3*T^8 - 76*T^7 - 171*T^6 + 1695*T^5 + 1612*T^4 - 14373*T^3 + 2457*T^2 + 33323*T - 24074
$41$
\( T^{9} - 4 T^{8} - 97 T^{7} + \cdots - 26568 \)
T^9 - 4*T^8 - 97*T^7 + 173*T^6 + 1836*T^5 - 2451*T^4 - 10899*T^3 + 14220*T^2 + 19656*T - 26568
$43$
\( T^{9} - 5 T^{8} - 245 T^{7} + \cdots - 7574992 \)
T^9 - 5*T^8 - 245*T^7 + 1330*T^6 + 16943*T^5 - 99454*T^4 - 288457*T^3 + 1809646*T^2 + 845596*T - 7574992
$47$
\( T^{9} - 25 T^{8} + 77 T^{7} + \cdots - 48492 \)
T^9 - 25*T^8 + 77*T^7 + 2948*T^6 - 35094*T^5 + 154995*T^4 - 255654*T^3 - 73716*T^2 + 472887*T - 48492
$53$
\( T^{9} - 18 T^{8} - 3 T^{7} + \cdots + 41688 \)
T^9 - 18*T^8 - 3*T^7 + 1279*T^6 - 2358*T^5 - 28893*T^4 + 37041*T^3 + 210822*T^2 + 176940*T + 41688
$59$
\( T^{9} + 6 T^{8} - 160 T^{7} + \cdots + 7776 \)
T^9 + 6*T^8 - 160*T^7 - 103*T^6 + 8127*T^5 - 29262*T^4 + 369*T^3 + 135666*T^2 - 161271*T + 7776
$61$
\( T^{9} - 26 T^{8} + 195 T^{7} + \cdots + 6452 \)
T^9 - 26*T^8 + 195*T^7 - 8*T^6 - 5005*T^5 + 11835*T^4 + 29348*T^3 - 94682*T^2 + 2793*T + 6452
$67$
\( T^{9} + 2 T^{8} - 78 T^{7} + \cdots - 4016 \)
T^9 + 2*T^8 - 78*T^7 - 270*T^6 + 862*T^5 + 4671*T^4 + 4611*T^3 - 4528*T^2 - 9564*T - 4016
$71$
\( T^{9} - 18 T^{8} + 15 T^{7} + \cdots - 2592 \)
T^9 - 18*T^8 + 15*T^7 + 1540*T^6 - 11685*T^5 + 31710*T^4 - 27207*T^3 - 9360*T^2 + 13500*T - 2592
$73$
\( T^{9} + 5 T^{8} - 355 T^{7} + \cdots + 2032304 \)
T^9 + 5*T^8 - 355*T^7 - 1622*T^6 + 28828*T^5 + 116695*T^4 - 468895*T^3 - 1500766*T^2 + 1694564*T + 2032304
$79$
\( T^{9} - 18 T^{8} - 129 T^{7} + \cdots - 3994384 \)
T^9 - 18*T^8 - 129*T^7 + 4342*T^6 - 23916*T^5 - 63714*T^4 + 1106075*T^3 - 4293816*T^2 + 6988188*T - 3994384
$83$
\( T^{9} - 13 T^{8} + \cdots - 300861216 \)
T^9 - 13*T^8 - 503*T^7 + 6196*T^6 + 77868*T^5 - 835191*T^4 - 4359906*T^3 + 33697782*T^2 + 54882765*T - 300861216
$89$
\( T^{9} - 9 T^{8} + \cdots - 1760749326 \)
T^9 - 9*T^8 - 624*T^7 + 5669*T^6 + 127572*T^5 - 1180344*T^4 - 9298305*T^3 + 87599736*T^2 + 181794861*T - 1760749326
$97$
\( T^{9} + 18 T^{8} - 52 T^{7} + \cdots - 507898 \)
T^9 + 18*T^8 - 52*T^7 - 2534*T^6 - 9600*T^5 + 68944*T^4 + 538040*T^3 + 1067025*T^2 + 338465*T - 507898
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