[N,k,chi] = [201,4,Mod(1,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("201.1");
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
\(3\)
\(-1\)
\(67\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} + 5T_{2}^{5} - 18T_{2}^{4} - 80T_{2}^{3} + 105T_{2}^{2} + 263T_{2} - 284 \)
T2^6 + 5*T2^5 - 18*T2^4 - 80*T2^3 + 105*T2^2 + 263*T2 - 284
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(201))\).
$p$
$F_p(T)$
$2$
\( T^{6} + 5 T^{5} - 18 T^{4} - 80 T^{3} + \cdots - 284 \)
T^6 + 5*T^5 - 18*T^4 - 80*T^3 + 105*T^2 + 263*T - 284
$3$
\( (T - 3)^{6} \)
(T - 3)^6
$5$
\( T^{6} + 12 T^{5} - 300 T^{4} + \cdots + 180036 \)
T^6 + 12*T^5 - 300*T^4 - 3798*T^3 + 621*T^2 + 100656*T + 180036
$7$
\( T^{6} + 62 T^{5} + 1044 T^{4} + \cdots + 136506 \)
T^6 + 62*T^5 + 1044*T^4 - 424*T^3 - 101363*T^2 - 217194*T + 136506
$11$
\( T^{6} + 72 T^{5} + \cdots + 291026784 \)
T^6 + 72*T^5 - 256*T^4 - 96156*T^3 - 1018952*T^2 + 22543536*T + 291026784
$13$
\( T^{6} + 192 T^{5} + \cdots + 931980112 \)
T^6 + 192*T^5 + 11010*T^4 + 69400*T^3 - 9160824*T^2 - 117245784*T + 931980112
$17$
\( T^{6} + 100 T^{5} + \cdots - 37296518336 \)
T^6 + 100*T^5 - 12072*T^4 - 1131820*T^3 + 42401280*T^2 + 3163253584*T - 37296518336
$19$
\( T^{6} + 266 T^{5} + \cdots - 10918171712 \)
T^6 + 266*T^5 + 1112*T^4 - 4886332*T^3 - 440104912*T^2 - 11193040144*T - 10918171712
$23$
\( T^{6} - 50 T^{5} + \cdots + 326139706 \)
T^6 - 50*T^5 - 13422*T^4 + 587762*T^3 - 3820143*T^2 - 46395302*T + 326139706
$29$
\( T^{6} + 242 T^{5} + \cdots + 106089693184 \)
T^6 + 242*T^5 - 36150*T^4 - 8501816*T^3 - 47597664*T^2 + 7624167296*T + 106089693184
$31$
\( T^{6} + 438 T^{5} + \cdots - 2597606002574 \)
T^6 + 438*T^5 - 11568*T^4 - 17355616*T^3 - 196190859*T^2 + 140805671730*T - 2597606002574
$37$
\( T^{6} + 596 T^{5} + \cdots + 1310694126564 \)
T^6 + 596*T^5 + 68070*T^4 - 9259660*T^3 - 907429463*T^2 + 36983842020*T + 1310694126564
$41$
\( T^{6} - 54 T^{5} + \cdots + 8708288608008 \)
T^6 - 54*T^5 - 251884*T^4 + 10126740*T^3 + 8805193489*T^2 - 777822252516*T + 8708288608008
$43$
\( T^{6} + \cdots - 153851666161248 \)
T^6 + 360*T^5 - 311526*T^4 - 95116680*T^3 + 24895966365*T^2 + 5722948559736*T - 153851666161248
$47$
\( T^{6} + \cdots + 556675819402176 \)
T^6 + 720*T^5 - 225934*T^4 - 248067384*T^3 - 40971091328*T^2 + 1923019138632*T + 556675819402176
$53$
\( T^{6} + \cdots - 246603742693452 \)
T^6 - 694*T^5 - 228272*T^4 + 109716480*T^3 + 34908219597*T^2 + 962385641424*T - 246603742693452
$59$
\( T^{6} + 378 T^{5} + \cdots + 27\!\cdots\!44 \)
T^6 + 378*T^5 - 527772*T^4 - 267218028*T^3 + 13790100717*T^2 + 22303036424484*T + 2707681698775944
$61$
\( T^{6} + \cdots - 409773359945408 \)
T^6 + 1396*T^5 + 615338*T^4 + 43289152*T^3 - 34065768112*T^2 - 7734367126328*T - 409773359945408
$67$
\( (T + 67)^{6} \)
(T + 67)^6
$71$
\( T^{6} + \cdots + 591280964816128 \)
T^6 + 964*T^5 - 470502*T^4 - 504948232*T^3 - 101621088192*T^2 - 1154762638328*T + 591280964816128
$73$
\( T^{6} + 192 T^{5} + \cdots - 21\!\cdots\!52 \)
T^6 + 192*T^5 - 1498494*T^4 - 71540860*T^3 + 595563093921*T^2 - 56850347312220*T - 21615544034197052
$79$
\( T^{6} + 802 T^{5} + \cdots - 26\!\cdots\!48 \)
T^6 + 802*T^5 - 1020190*T^4 - 504998504*T^3 + 371724786896*T^2 + 34957761653152*T - 26857452424898048
$83$
\( T^{6} - 2126 T^{5} + \cdots + 30\!\cdots\!68 \)
T^6 - 2126*T^5 + 33072*T^4 + 1930344272*T^3 - 562341276171*T^2 - 298254336629120*T + 30763684475967568
$89$
\( T^{6} - 432 T^{5} + \cdots - 38\!\cdots\!08 \)
T^6 - 432*T^5 - 3137452*T^4 + 167541516*T^3 + 2905026582568*T^2 + 637645267019088*T - 385242146035999008
$97$
\( T^{6} - 1290 T^{5} + \cdots + 12\!\cdots\!08 \)
T^6 - 1290*T^5 - 1555116*T^4 + 1106982052*T^3 + 1000555551048*T^2 + 211592119579440*T + 12434831538987808
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