[N,k,chi] = [102,6,Mod(1,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.1");
S:= CuspForms(chi, 6);
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(17\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 53T_{5}^{2} - 3632T_{5} + 156684 \)
T5^3 - 53*T5^2 - 3632*T5 + 156684
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(102))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{3} \)
(T - 4)^3
$3$
\( (T - 9)^{3} \)
(T - 9)^3
$5$
\( T^{3} - 53 T^{2} - 3632 T + 156684 \)
T^3 - 53*T^2 - 3632*T + 156684
$7$
\( T^{3} - 168 T^{2} - 7024 T + 254592 \)
T^3 - 168*T^2 - 7024*T + 254592
$11$
\( T^{3} - 365 T^{2} + \cdots + 174150000 \)
T^3 - 365*T^2 - 456600*T + 174150000
$13$
\( T^{3} - 663 T^{2} + \cdots - 15142380 \)
T^3 - 663*T^2 - 231304*T - 15142380
$17$
\( (T - 289)^{3} \)
(T - 289)^3
$19$
\( T^{3} - 1777 T^{2} + \cdots + 10823035696 \)
T^3 - 1777*T^2 - 5859832*T + 10823035696
$23$
\( T^{3} - 573 T^{2} + \cdots + 6154132464 \)
T^3 - 573*T^2 - 6838992*T + 6154132464
$29$
\( T^{3} - 1278 T^{2} + \cdots + 8425642584 \)
T^3 - 1278*T^2 - 5614132*T + 8425642584
$31$
\( T^{3} + 2078 T^{2} + \cdots - 189692148384 \)
T^3 + 2078*T^2 - 55366832*T - 189692148384
$37$
\( T^{3} - 3428 T^{2} + \cdots + 756189044384 \)
T^3 - 3428*T^2 - 246581932*T + 756189044384
$41$
\( T^{3} + 121 T^{2} + \cdots + 599247187860 \)
T^3 + 121*T^2 - 248305760*T + 599247187860
$43$
\( T^{3} + 6521 T^{2} + \cdots + 1051734223248 \)
T^3 + 6521*T^2 - 245740760*T + 1051734223248
$47$
\( T^{3} + 11266 T^{2} + \cdots + 725716865664 \)
T^3 + 11266*T^2 - 302874816*T + 725716865664
$53$
\( T^{3} + 12898 T^{2} + \cdots - 2618974153224 \)
T^3 + 12898*T^2 - 253931460*T - 2618974153224
$59$
\( T^{3} + 39618 T^{2} + \cdots + 2026881400608 \)
T^3 + 39618*T^2 + 501653376*T + 2026881400608
$61$
\( T^{3} + 17040 T^{2} + \cdots - 14077185611408 \)
T^3 + 17040*T^2 - 864644028*T - 14077185611408
$67$
\( T^{3} + \cdots - 130615297281216 \)
T^3 + 18220*T^2 - 4107038352*T - 130615297281216
$71$
\( T^{3} + 98124 T^{2} + \cdots + 34278499449792 \)
T^3 + 98124*T^2 + 3186956880*T + 34278499449792
$73$
\( T^{3} + 47590 T^{2} + \cdots + 10516757566376 \)
T^3 + 47590*T^2 - 1681762852*T + 10516757566376
$79$
\( T^{3} + \cdots - 227350425704480 \)
T^3 + 27302*T^2 - 5757204400*T - 227350425704480
$83$
\( T^{3} + \cdots + 155380242235680 \)
T^3 + 182354*T^2 + 10131686304*T + 155380242235680
$89$
\( T^{3} + 199528 T^{2} + \cdots - 31426154645904 \)
T^3 + 199528*T^2 + 7889556660*T - 31426154645904
$97$
\( T^{3} + \cdots + 315785543467872 \)
T^3 - 91500*T^2 - 16226939548*T + 315785543467872
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