[N,k,chi] = [3016,2,Mod(1,3016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3016.1");
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
\(2\)
\(1\)
\(13\)
\(-1\)
\(29\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{10} - 2 T_{3}^{9} - 21 T_{3}^{8} + 40 T_{3}^{7} + 138 T_{3}^{6} - 243 T_{3}^{5} - 318 T_{3}^{4} + 448 T_{3}^{3} + 312 T_{3}^{2} - 240 T_{3} - 128 \)
T3^10 - 2*T3^9 - 21*T3^8 + 40*T3^7 + 138*T3^6 - 243*T3^5 - 318*T3^4 + 448*T3^3 + 312*T3^2 - 240*T3 - 128
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3016))\).
$p$
$F_p(T)$
$2$
\( T^{10} \)
T^10
$3$
\( T^{10} - 2 T^{9} - 21 T^{8} + 40 T^{7} + \cdots - 128 \)
T^10 - 2*T^9 - 21*T^8 + 40*T^7 + 138*T^6 - 243*T^5 - 318*T^4 + 448*T^3 + 312*T^2 - 240*T - 128
$5$
\( T^{10} - 5 T^{9} - 25 T^{8} + 139 T^{7} + \cdots - 344 \)
T^10 - 5*T^9 - 25*T^8 + 139*T^7 + 169*T^6 - 1182*T^5 - 243*T^4 + 3285*T^3 + 130*T^2 - 2452*T - 344
$7$
\( T^{10} + 2 T^{9} - 33 T^{8} - 60 T^{7} + \cdots + 32 \)
T^10 + 2*T^9 - 33*T^8 - 60*T^7 + 338*T^6 + 554*T^5 - 1164*T^4 - 1431*T^3 + 1348*T^2 + 900*T + 32
$11$
\( T^{10} - 4 T^{9} - 52 T^{8} + \cdots + 2312 \)
T^10 - 4*T^9 - 52*T^8 + 168*T^7 + 954*T^6 - 1927*T^5 - 7492*T^4 + 3817*T^3 + 19550*T^2 + 12716*T + 2312
$13$
\( (T - 1)^{10} \)
(T - 1)^10
$17$
\( T^{10} - 10 T^{9} - 86 T^{8} + \cdots + 628576 \)
T^10 - 10*T^9 - 86*T^8 + 981*T^7 + 2058*T^6 - 30411*T^5 - 10804*T^4 + 324356*T^3 - 27368*T^2 - 949280*T + 628576
$19$
\( T^{10} + T^{9} - 120 T^{8} + \cdots - 455848 \)
T^10 + T^9 - 120*T^8 - 292*T^7 + 4325*T^6 + 14989*T^5 - 37572*T^4 - 136803*T^3 + 172034*T^2 + 382604*T - 455848
$23$
\( T^{10} - 23 T^{9} + 187 T^{8} + \cdots - 9728 \)
T^10 - 23*T^9 + 187*T^8 - 543*T^7 - 574*T^6 + 5955*T^5 - 6470*T^4 - 12356*T^3 + 18464*T^2 + 8896*T - 9728
$29$
\( (T + 1)^{10} \)
(T + 1)^10
$31$
\( T^{10} + 13 T^{9} - 63 T^{8} + \cdots - 29056 \)
T^10 + 13*T^9 - 63*T^8 - 1575*T^7 - 5442*T^6 + 15163*T^5 + 85530*T^4 - 46900*T^3 - 345288*T^2 + 207648*T - 29056
$37$
\( T^{10} + 7 T^{9} - 68 T^{8} + \cdots + 1045504 \)
T^10 + 7*T^9 - 68*T^8 - 545*T^7 + 1365*T^6 + 15057*T^5 - 2516*T^4 - 172772*T^3 - 161056*T^2 + 685760*T + 1045504
$41$
\( T^{10} - 16 T^{9} - 131 T^{8} + \cdots + 2453504 \)
T^10 - 16*T^9 - 131*T^8 + 2804*T^7 + 2486*T^6 - 151390*T^5 + 158978*T^4 + 2422909*T^3 - 2862488*T^2 - 2253104*T + 2453504
$43$
\( T^{10} + 12 T^{9} - 97 T^{8} + \cdots - 15872 \)
T^10 + 12*T^9 - 97*T^8 - 1146*T^7 + 2932*T^6 + 19855*T^5 - 68700*T^4 + 33556*T^3 + 66976*T^2 - 42304*T - 15872
$47$
\( T^{10} - 11 T^{9} - 143 T^{8} + \cdots + 172448 \)
T^10 - 11*T^9 - 143*T^8 + 1763*T^7 + 1830*T^6 - 47157*T^5 - 2008*T^4 + 408940*T^3 - 50184*T^2 - 1117920*T + 172448
$53$
\( T^{10} - 11 T^{9} + \cdots + 148185504 \)
T^10 - 11*T^9 - 336*T^8 + 3983*T^7 + 30997*T^6 - 432781*T^5 - 386484*T^4 + 13111708*T^3 - 13939368*T^2 - 91033056*T + 148185504
$59$
\( T^{10} + 11 T^{9} - 272 T^{8} + \cdots - 79055104 \)
T^10 + 11*T^9 - 272*T^8 - 3733*T^7 + 15115*T^6 + 373579*T^5 + 830232*T^4 - 9703496*T^3 - 60408912*T^2 - 122791504*T - 79055104
$61$
\( T^{10} - 34 T^{9} + 383 T^{8} + \cdots - 584 \)
T^10 - 34*T^9 + 383*T^8 - 1356*T^7 - 3816*T^6 + 34892*T^5 - 55500*T^4 - 28193*T^3 + 71234*T^2 + 20036*T - 584
$67$
\( T^{10} + 23 T^{9} - 95 T^{8} + \cdots + 19559552 \)
T^10 + 23*T^9 - 95*T^8 - 5213*T^7 - 20490*T^6 + 256333*T^5 + 1966262*T^4 + 1337832*T^3 - 17543752*T^2 - 28892944*T + 19559552
$71$
\( T^{10} + 4 T^{9} + \cdots + 1890479104 \)
T^10 + 4*T^9 - 465*T^8 - 2708*T^7 + 72070*T^6 + 555041*T^5 - 3816664*T^4 - 41141548*T^3 + 3426352*T^2 + 832347776*T + 1890479104
$73$
\( T^{10} - 39 T^{9} + 509 T^{8} + \cdots + 55296 \)
T^10 - 39*T^9 + 509*T^8 - 1969*T^7 - 9383*T^6 + 91970*T^5 - 204581*T^4 - 21727*T^3 + 510528*T^2 - 440352*T + 55296
$79$
\( T^{10} - 5 T^{9} - 178 T^{8} + \cdots + 944 \)
T^10 - 5*T^9 - 178*T^8 + 478*T^7 + 7621*T^6 + 3941*T^5 - 42882*T^4 - 8347*T^3 + 27712*T^2 + 10764*T + 944
$83$
\( T^{10} - 6 T^{9} - 381 T^{8} + \cdots - 71552 \)
T^10 - 6*T^9 - 381*T^8 + 1093*T^7 + 42729*T^6 - 29647*T^5 - 1222366*T^4 + 265736*T^3 + 2683832*T^2 - 817552*T - 71552
$89$
\( T^{10} + 24 T^{9} + \cdots - 316752512 \)
T^10 + 24*T^9 - 142*T^8 - 5433*T^7 + 8725*T^6 + 436142*T^5 - 827688*T^4 - 13879965*T^3 + 42015520*T^2 + 88395504*T - 316752512
$97$
\( T^{10} - 19 T^{9} - 318 T^{8} + \cdots - 38534656 \)
T^10 - 19*T^9 - 318*T^8 + 7108*T^7 + 20385*T^6 - 744033*T^5 - 197956*T^4 + 30590695*T^3 - 6011688*T^2 - 442550800*T - 38534656
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