[N,k,chi] = [121,4,Mod(1,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, 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("121.1");
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
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} + 4T_{2}^{3} - 15T_{2}^{2} - 38T_{2} + 44 \)
T2^4 + 4*T2^3 - 15*T2^2 - 38*T2 + 44
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(121))\).
$p$
$F_p(T)$
$2$
\( T^{4} + 4 T^{3} - 15 T^{2} - 38 T + 44 \)
T^4 + 4*T^3 - 15*T^2 - 38*T + 44
$3$
\( (T^{2} - 3 T - 7)^{2} \)
(T^2 - 3*T - 7)^2
$5$
\( T^{4} + 11 T^{3} - 183 T^{2} + \cdots + 8036 \)
T^4 + 11*T^3 - 183*T^2 - 826*T + 8036
$7$
\( T^{4} + 25 T^{3} - 251 T^{2} + \cdots - 396 \)
T^4 + 25*T^3 - 251*T^2 - 720*T - 396
$11$
\( T^{4} \)
T^4
$13$
\( T^{4} + 25 T^{3} - 2215 T^{2} + \cdots - 53900 \)
T^4 + 25*T^3 - 2215*T^2 + 21350*T - 53900
$17$
\( T^{4} + 232 T^{3} + 18185 T^{2} + \cdots + 3099789 \)
T^4 + 232*T^3 + 18185*T^2 + 523404*T + 3099789
$19$
\( T^{4} + 154 T^{3} + 501 T^{2} + \cdots - 9492329 \)
T^4 + 154*T^3 + 501*T^2 - 417956*T - 9492329
$23$
\( T^{4} + 6 T^{3} - 21180 T^{2} + \cdots + 49883584 \)
T^4 + 6*T^3 - 21180*T^2 + 538608*T + 49883584
$29$
\( T^{4} + 363 T^{3} + \cdots - 98528364 \)
T^4 + 363*T^3 + 22123*T^2 - 2129292*T - 98528364
$31$
\( T^{4} - 37 T^{3} - 57125 T^{2} + \cdots - 33222196 \)
T^4 - 37*T^3 - 57125*T^2 + 6128976*T - 33222196
$37$
\( T^{4} - 93 T^{3} + \cdots + 163244164 \)
T^4 - 93*T^3 - 26715*T^2 + 1301514*T + 163244164
$41$
\( T^{4} + 152 T^{3} + \cdots + 1659084581 \)
T^4 + 152*T^3 - 85167*T^2 - 6085828*T + 1659084581
$43$
\( T^{4} - 325 T^{3} + \cdots - 1288748736 \)
T^4 - 325*T^3 - 77011*T^2 + 29170680*T - 1288748736
$47$
\( T^{4} + 869 T^{3} + \cdots + 837687536 \)
T^4 + 869*T^3 + 243921*T^2 + 26240564*T + 837687536
$53$
\( T^{4} - 811 T^{3} + \cdots - 847714576 \)
T^4 - 811*T^3 + 83175*T^2 + 17688932*T - 847714576
$59$
\( T^{4} - 178 T^{3} + \cdots + 258148219 \)
T^4 - 178*T^3 - 76315*T^2 - 654836*T + 258148219
$61$
\( T^{4} - 105 T^{3} + \cdots + 47885889744 \)
T^4 - 105*T^3 - 547281*T^2 + 78348060*T + 47885889744
$67$
\( T^{4} - 43 T^{3} + \cdots - 8869996224 \)
T^4 - 43*T^3 - 394721*T^2 - 116831232*T - 8869996224
$71$
\( T^{4} - 629 T^{3} + \cdots - 744521796 \)
T^4 - 629*T^3 - 324055*T^2 - 36188442*T - 744521796
$73$
\( T^{4} - 270 T^{3} + \cdots + 38050128809 \)
T^4 - 270*T^3 - 640429*T^2 - 47158090*T + 38050128809
$79$
\( T^{4} + 977 T^{3} + \cdots - 210591964 \)
T^4 + 977*T^3 + 67063*T^2 - 94696308*T - 210591964
$83$
\( T^{4} + 1686 T^{3} + \cdots - 181259356509 \)
T^4 + 1686*T^3 - 164459*T^2 - 1047672444*T - 181259356509
$89$
\( T^{4} - 1891 T^{3} + \cdots - 2046678844 \)
T^4 - 1891*T^3 + 858267*T^2 - 9000124*T - 2046678844
$97$
\( T^{4} + 1772 T^{3} + \cdots - 357121332099 \)
T^4 + 1772*T^3 + 94013*T^2 - 960815688*T - 357121332099
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