[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
\( T_{3}^{9} - 3T_{3}^{8} - 16T_{3}^{7} + 46T_{3}^{6} + 82T_{3}^{5} - 216T_{3}^{4} - 155T_{3}^{3} + 334T_{3}^{2} + 84T_{3} - 112 \)
T3^9 - 3*T3^8 - 16*T3^7 + 46*T3^6 + 82*T3^5 - 216*T3^4 - 155*T3^3 + 334*T3^2 + 84*T3 - 112
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{9} \)
(T - 1)^9
$3$
\( T^{9} - 3 T^{8} - 16 T^{7} + 46 T^{6} + \cdots - 112 \)
T^9 - 3*T^8 - 16*T^7 + 46*T^6 + 82*T^5 - 216*T^4 - 155*T^3 + 334*T^2 + 84*T - 112
$5$
\( (T - 1)^{9} \)
(T - 1)^9
$7$
\( T^{9} - 9 T^{8} + 5 T^{7} + 144 T^{6} + \cdots - 2520 \)
T^9 - 9*T^8 + 5*T^7 + 144*T^6 - 264*T^5 - 719*T^4 + 1438*T^3 + 1850*T^2 - 2373*T - 2520
$11$
\( T^{9} - 10 T^{8} + 5 T^{7} + 158 T^{6} + \cdots + 560 \)
T^9 - 10*T^8 + 5*T^7 + 158*T^6 - 104*T^5 - 998*T^4 - 91*T^3 + 2358*T^2 + 2212*T + 560
$13$
\( (T - 1)^{9} \)
(T - 1)^9
$17$
\( T^{9} - T^{8} - 50 T^{7} + T^{6} + \cdots - 954 \)
T^9 - T^8 - 50*T^7 + T^6 + 732*T^5 + 322*T^4 - 3175*T^3 - 832*T^2 + 3201*T - 954
$19$
\( T^{9} - 10 T^{8} - 29 T^{7} + \cdots - 6308 \)
T^9 - 10*T^8 - 29*T^7 + 434*T^6 - 8*T^5 - 4877*T^4 + 3348*T^3 + 15787*T^2 - 11831*T - 6308
$23$
\( T^{9} - 8 T^{8} - 56 T^{7} + \cdots + 36008 \)
T^9 - 8*T^8 - 56*T^7 + 659*T^6 - 777*T^5 - 8320*T^4 + 26027*T^3 - 7572*T^2 - 44487*T + 36008
$29$
\( T^{9} - 9 T^{8} - 50 T^{7} + \cdots + 19350 \)
T^9 - 9*T^8 - 50*T^7 + 619*T^6 - 386*T^5 - 8268*T^4 + 17157*T^3 + 10012*T^2 - 38433*T + 19350
$31$
\( (T + 1)^{9} \)
(T + 1)^9
$37$
\( T^{9} + 3 T^{8} - 78 T^{7} + \cdots - 38102 \)
T^9 + 3*T^8 - 78*T^7 - 159*T^6 + 2035*T^5 + 1660*T^4 - 20707*T^3 + 7503*T^2 + 51723*T - 38102
$41$
\( T^{9} - 51 T^{7} + 17 T^{6} + 424 T^{5} + \cdots - 40 \)
T^9 - 51*T^7 + 17*T^6 + 424*T^5 + 155*T^4 - 805*T^3 - 916*T^2 - 344*T - 40
$43$
\( T^{9} - 7 T^{8} - 105 T^{7} + \cdots + 715568 \)
T^9 - 7*T^8 - 105*T^7 + 842*T^6 + 2701*T^5 - 32484*T^4 + 21067*T^3 + 380386*T^2 - 1033004*T + 715568
$47$
\( T^{9} - 7 T^{8} - 153 T^{7} + \cdots + 166160 \)
T^9 - 7*T^8 - 153*T^7 + 1220*T^6 + 4958*T^5 - 55259*T^4 + 51872*T^3 + 410728*T^2 - 836091*T + 166160
$53$
\( T^{9} - 8 T^{8} - 175 T^{7} + \cdots - 27640 \)
T^9 - 8*T^8 - 175*T^7 + 999*T^6 + 7746*T^5 - 33769*T^4 - 115953*T^3 + 295290*T^2 + 667892*T - 27640
$59$
\( T^{9} - 2 T^{8} - 316 T^{7} + \cdots + 8513900 \)
T^9 - 2*T^8 - 316*T^7 + 1545*T^6 + 28507*T^5 - 217704*T^4 - 380201*T^3 + 6844946*T^2 - 17135725*T + 8513900
$61$
\( T^{9} + 2 T^{8} - 221 T^{7} + \cdots + 42322 \)
T^9 + 2*T^8 - 221*T^7 + 400*T^6 + 12285*T^5 - 45317*T^4 - 153986*T^3 + 871664*T^2 - 881383*T + 42322
$67$
\( T^{9} - 18 T^{8} - 156 T^{7} + \cdots - 10707728 \)
T^9 - 18*T^8 - 156*T^7 + 3286*T^6 + 9330*T^5 - 181685*T^4 - 398749*T^3 + 3192800*T^2 + 6198164*T - 10707728
$71$
\( T^{9} - 14 T^{8} - 389 T^{7} + \cdots + 43268384 \)
T^9 - 14*T^8 - 389*T^7 + 5412*T^6 + 44387*T^5 - 535998*T^4 - 2716027*T^3 + 16398344*T^2 + 83176156*T + 43268384
$73$
\( T^{9} - T^{8} - 269 T^{7} + \cdots + 5387144 \)
T^9 - T^8 - 269*T^7 + 32*T^6 + 22224*T^5 + 21275*T^4 - 564883*T^3 - 1088632*T^2 + 2714224*T + 5387144
$79$
\( T^{9} - 6 T^{8} - 227 T^{7} + \cdots - 152000 \)
T^9 - 6*T^8 - 227*T^7 + 1548*T^6 + 11840*T^5 - 93212*T^4 + 19059*T^3 + 347100*T^2 + 82284*T - 152000
$83$
\( T^{9} - 7 T^{8} - 431 T^{7} + \cdots + 96523092 \)
T^9 - 7*T^8 - 431*T^7 + 1602*T^6 + 59986*T^5 - 62043*T^4 - 3220274*T^3 - 3305492*T^2 + 48360495*T + 96523092
$89$
\( T^{9} + 19 T^{8} - 66 T^{7} + \cdots - 790346 \)
T^9 + 19*T^8 - 66*T^7 - 4027*T^6 - 34476*T^5 - 96214*T^4 + 94093*T^3 + 768574*T^2 + 393417*T - 790346
$97$
\( T^{9} + 6 T^{8} - 434 T^{7} + \cdots - 10716566 \)
T^9 + 6*T^8 - 434*T^7 - 3344*T^6 + 40592*T^5 + 375846*T^4 - 74506*T^3 - 6510579*T^2 - 15683591*T - 10716566
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