[N,k,chi] = [112,10,Mod(1,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.1");
S:= CuspForms(chi, 10);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2305}\).
We also show the integral \(q\)-expansion of the trace form .
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
\(2\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 14T_{3} - 57576 \)
T3^2 - 14*T3 - 57576
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(112))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 14T - 57576 \)
T^2 - 14*T - 57576
$5$
\( T^{2} + 2730 T + 846720 \)
T^2 + 2730*T + 846720
$7$
\( (T + 2401)^{2} \)
(T + 2401)^2
$11$
\( T^{2} + 44940 T - 2036361600 \)
T^2 + 44940*T - 2036361600
$13$
\( T^{2} - 100282 T + 2397429256 \)
T^2 - 100282*T + 2397429256
$17$
\( T^{2} + 870408 T + 183575251116 \)
T^2 + 870408*T + 183575251116
$19$
\( T^{2} + 508774 T - 352577596856 \)
T^2 + 508774*T - 352577596856
$23$
\( T^{2} + 79800 T - 115915968000 \)
T^2 + 79800*T - 115915968000
$29$
\( T^{2} - 2006328 T - 31904129519604 \)
T^2 - 2006328*T - 31904129519604
$31$
\( T^{2} + 2188732 T - 2367849772544 \)
T^2 + 2188732*T - 2367849772544
$37$
\( T^{2} + 20723576 T + 60225113026444 \)
T^2 + 20723576*T + 60225113026444
$41$
\( T^{2} + \cdots - 527816477266884 \)
T^2 - 19016592*T - 527816477266884
$43$
\( T^{2} + \cdots - 271341247682336 \)
T^2 + 4193716*T - 271341247682336
$47$
\( T^{2} - 74542524 T + 12\!\cdots\!44 \)
T^2 - 74542524*T + 1296550084878144
$53$
\( T^{2} + \cdots - 494746212296124 \)
T^2 + 3239748*T - 494746212296124
$59$
\( T^{2} - 133642362 T + 15\!\cdots\!36 \)
T^2 - 133642362*T + 1575046316366136
$61$
\( T^{2} - 227801686 T + 11\!\cdots\!24 \)
T^2 - 227801686*T + 11243934945943024
$67$
\( T^{2} + 332930272 T + 21\!\cdots\!96 \)
T^2 + 332930272*T + 21401918313456496
$71$
\( T^{2} - 167985720 T - 85\!\cdots\!00 \)
T^2 - 167985720*T - 85127259938918400
$73$
\( T^{2} + 44684276 T - 83\!\cdots\!56 \)
T^2 + 44684276*T - 83678371011966956
$79$
\( T^{2} + 269642776 T + 68\!\cdots\!44 \)
T^2 + 269642776*T + 6880003984764544
$83$
\( T^{2} - 183105762 T - 76\!\cdots\!64 \)
T^2 - 183105762*T - 76697718543013464
$89$
\( T^{2} - 791657748 T + 50\!\cdots\!76 \)
T^2 - 791657748*T + 50565747709419876
$97$
\( T^{2} + 4169480 T - 45\!\cdots\!00 \)
T^2 + 4169480*T - 451110491471642900
show more
show less