[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
\( T_{3}^{7} - 3T_{3}^{6} - 8T_{3}^{5} + 24T_{3}^{4} + 18T_{3}^{3} - 48T_{3}^{2} - 9T_{3} + 4 \)
T3^7 - 3*T3^6 - 8*T3^5 + 24*T3^4 + 18*T3^3 - 48*T3^2 - 9*T3 + 4
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{7} \)
(T + 1)^7
$3$
\( T^{7} - 3 T^{6} - 8 T^{5} + 24 T^{4} + \cdots + 4 \)
T^7 - 3*T^6 - 8*T^5 + 24*T^4 + 18*T^3 - 48*T^2 - 9*T + 4
$5$
\( (T + 1)^{7} \)
(T + 1)^7
$7$
\( T^{7} - 2 T^{6} - 22 T^{5} + 40 T^{4} + \cdots + 432 \)
T^7 - 2*T^6 - 22*T^5 + 40*T^4 + 148*T^3 - 237*T^2 - 315*T + 432
$11$
\( T^{7} + 6 T^{6} - 21 T^{5} - 144 T^{4} + \cdots - 28 \)
T^7 + 6*T^6 - 21*T^5 - 144*T^4 - 18*T^3 + 278*T^2 - 83*T - 28
$13$
\( (T + 1)^{7} \)
(T + 1)^7
$17$
\( T^{7} - 41 T^{5} - 74 T^{4} + \cdots - 134 \)
T^7 - 41*T^5 - 74*T^4 + 225*T^3 + 407*T^2 - 253*T - 134
$19$
\( T^{7} + 9 T^{6} - 15 T^{5} + \cdots + 1800 \)
T^7 + 9*T^6 - 15*T^5 - 312*T^4 - 437*T^3 + 2314*T^2 + 5685*T + 1800
$23$
\( T^{7} - 7 T^{6} - 60 T^{5} + \cdots - 2808 \)
T^7 - 7*T^6 - 60*T^5 + 246*T^4 + 1467*T^3 - 271*T^2 - 5643*T - 2808
$29$
\( T^{7} + 4 T^{6} - 95 T^{5} - 262 T^{4} + \cdots + 338 \)
T^7 + 4*T^6 - 95*T^5 - 262*T^4 + 1693*T^3 + 3855*T^2 - 2555*T + 338
$31$
\( (T + 1)^{7} \)
(T + 1)^7
$37$
\( T^{7} - 2 T^{6} - 75 T^{5} + \cdots + 4542 \)
T^7 - 2*T^6 - 75*T^5 + 206*T^4 + 764*T^3 - 1946*T^2 - 1947*T + 4542
$41$
\( T^{7} + 14 T^{6} - 9 T^{5} - 457 T^{4} + \cdots - 130 \)
T^7 + 14*T^6 - 9*T^5 - 457*T^4 - 122*T^3 + 1817*T^2 - 85*T - 130
$43$
\( T^{7} - 9 T^{6} - 97 T^{5} + \cdots + 225196 \)
T^7 - 9*T^6 - 97*T^5 + 828*T^4 + 2981*T^3 - 24068*T^2 - 29467*T + 225196
$47$
\( T^{7} + 8 T^{6} - 98 T^{5} + \cdots + 23064 \)
T^7 + 8*T^6 - 98*T^5 - 900*T^4 + 1200*T^3 + 24865*T^2 + 57585*T + 23064
$53$
\( T^{7} + 6 T^{6} - 195 T^{5} + \cdots - 27494 \)
T^7 + 6*T^6 - 195*T^5 - 1695*T^4 + 1818*T^3 + 46429*T^2 + 94365*T - 27494
$59$
\( T^{7} + 15 T^{6} - 238 T^{5} + \cdots - 1417312 \)
T^7 + 15*T^6 - 238*T^5 - 4054*T^4 + 9729*T^3 + 280687*T^2 + 530969*T - 1417312
$61$
\( T^{7} - T^{6} - 109 T^{5} + \cdots - 48594 \)
T^7 - T^6 - 109*T^5 - 46*T^4 + 3298*T^3 + 3505*T^2 - 29145*T - 48594
$67$
\( T^{7} - 14 T^{6} - 150 T^{5} + \cdots - 6948 \)
T^7 - 14*T^6 - 150*T^5 + 1442*T^4 + 8478*T^3 - 7685*T^2 - 41595*T - 6948
$71$
\( T^{7} + 16 T^{6} - 259 T^{5} + \cdots - 2002912 \)
T^7 + 16*T^6 - 259*T^5 - 5544*T^4 - 5477*T^3 + 292216*T^2 + 913191*T - 2002912
$73$
\( T^{7} + 13 T^{6} + 43 T^{5} - 22 T^{4} + \cdots + 30 \)
T^7 + 13*T^6 + 43*T^5 - 22*T^4 - 240*T^3 - 133*T^2 + 75*T + 30
$79$
\( T^{7} + 14 T^{6} + 27 T^{5} + \cdots + 2336 \)
T^7 + 14*T^6 + 27*T^5 - 300*T^4 - 930*T^3 + 1222*T^2 + 4305*T + 2336
$83$
\( T^{7} + 10 T^{6} - 98 T^{5} + \cdots - 6084 \)
T^7 + 10*T^6 - 98*T^5 - 506*T^4 + 2428*T^3 + 5669*T^2 - 15015*T - 6084
$89$
\( T^{7} + 26 T^{6} - 59 T^{5} + \cdots + 8157854 \)
T^7 + 26*T^6 - 59*T^5 - 6900*T^4 - 54255*T^3 + 129285*T^2 + 2823879*T + 8157854
$97$
\( T^{7} + 5 T^{6} - 526 T^{5} + \cdots - 14584478 \)
T^7 + 5*T^6 - 526*T^5 - 3951*T^4 + 68647*T^3 + 669076*T^2 - 824475*T - 14584478
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