[N,k,chi] = [152,4,Mod(1,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.1");
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{57})\).
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
\(2\)
\(-1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + T_{3} - 14 \)
T3^2 + T3 - 14
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(152))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + T - 14 \)
T^2 + T - 14
$5$
\( T^{2} + 5T - 8 \)
T^2 + 5*T - 8
$7$
\( T^{2} + 6T - 219 \)
T^2 + 6*T - 219
$11$
\( T^{2} + 15T - 642 \)
T^2 + 15*T - 642
$13$
\( T^{2} + 59T + 172 \)
T^2 + 59*T + 172
$17$
\( T^{2} + 104T + 1279 \)
T^2 + 104*T + 1279
$19$
\( (T + 19)^{2} \)
(T + 19)^2
$23$
\( T^{2} + 21T - 15408 \)
T^2 + 21*T - 15408
$29$
\( T^{2} + 137T + 3538 \)
T^2 + 137*T + 3538
$31$
\( T^{2} - 4T - 11168 \)
T^2 - 4*T - 11168
$37$
\( T^{2} + 152T - 5396 \)
T^2 + 152*T - 5396
$41$
\( T^{2} + 210T - 104400 \)
T^2 + 210*T - 104400
$43$
\( T^{2} - 67T - 6416 \)
T^2 - 67*T - 6416
$47$
\( T^{2} - 273T - 10224 \)
T^2 - 273*T - 10224
$53$
\( T^{2} - 209T + 10792 \)
T^2 - 209*T + 10792
$59$
\( T^{2} - 799T + 103042 \)
T^2 - 799*T + 103042
$61$
\( T^{2} - 149T - 34478 \)
T^2 - 149*T - 34478
$67$
\( T^{2} - 201T + 9744 \)
T^2 - 201*T + 9744
$71$
\( T^{2} - 792T + 14316 \)
T^2 - 792*T + 14316
$73$
\( T^{2} + 246T - 58743 \)
T^2 + 246*T - 58743
$79$
\( T^{2} + 254T - 169064 \)
T^2 + 254*T - 169064
$83$
\( T^{2} - 374T - 302984 \)
T^2 - 374*T - 302984
$89$
\( T^{2} + 564T - 467904 \)
T^2 + 564*T - 467904
$97$
\( T^{2} + 178 T - 1985312 \)
T^2 + 178*T - 1985312
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