[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, 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("2312.1");
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
\(2\)
\(1\)
\(17\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - T_{3}^{5} - 112T_{3}^{4} - 13T_{3}^{3} + 2192T_{3}^{2} + 359T_{3} - 1277 \)
T3^6 - T3^5 - 112*T3^4 - 13*T3^3 + 2192*T3^2 + 359*T3 - 1277
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2312))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} - T^{5} - 112 T^{4} - 13 T^{3} + \cdots - 1277 \)
T^6 - T^5 - 112*T^4 - 13*T^3 + 2192*T^2 + 359*T - 1277
$5$
\( T^{6} - 13 T^{5} - 246 T^{4} + \cdots + 392853 \)
T^6 - 13*T^5 - 246*T^4 + 3007*T^3 + 11042*T^2 - 171957*T + 392853
$7$
\( T^{6} - T^{5} - 870 T^{4} + \cdots + 819009 \)
T^6 - T^5 - 870*T^4 - 1673*T^3 + 188642*T^2 + 969207*T + 819009
$11$
\( T^{6} + 8 T^{5} + \cdots - 1017250773 \)
T^6 + 8*T^5 - 4471*T^4 + 976*T^3 + 4116747*T^2 - 532440*T - 1017250773
$13$
\( T^{6} + 33 T^{5} + \cdots - 904289589 \)
T^6 + 33*T^5 - 6156*T^4 - 101495*T^3 + 9745116*T^2 - 70372791*T - 904289589
$17$
\( T^{6} \)
T^6
$19$
\( T^{6} - 75 T^{5} + \cdots - 44823153543 \)
T^6 - 75*T^5 - 13566*T^4 + 1069085*T^3 + 29013834*T^2 - 1865019459*T - 44823153543
$23$
\( T^{6} - 155 T^{5} + \cdots - 554418546681 \)
T^6 - 155*T^5 - 38020*T^4 + 4618145*T^3 + 349663044*T^2 - 22693804683*T - 554418546681
$29$
\( T^{6} - 9 T^{5} + \cdots - 591728358573 \)
T^6 - 9*T^5 - 90132*T^4 + 2773775*T^3 + 1528775748*T^2 - 20092824609*T - 591728358573
$31$
\( T^{6} - 374 T^{5} + \cdots + 3269992954081 \)
T^6 - 374*T^5 - 51553*T^4 + 29437996*T^3 - 1078534657*T^2 - 293181923702*T + 3269992954081
$37$
\( T^{6} - 118 T^{5} + \cdots + 4855725817536 \)
T^6 - 118*T^5 - 142432*T^4 + 4096648*T^3 + 4311048576*T^2 + 313206415776*T + 4855725817536
$41$
\( T^{6} + 60 T^{5} + \cdots - 14245304766912 \)
T^6 + 60*T^5 - 262692*T^4 - 34793952*T^3 + 9963734256*T^2 + 785852554176*T - 14245304766912
$43$
\( T^{6} - 230 T^{5} + \cdots - 24\!\cdots\!07 \)
T^6 - 230*T^5 - 448657*T^4 + 89011180*T^3 + 60269505983*T^2 - 7871379737414*T - 2436803345929007
$47$
\( T^{6} - 276 T^{5} + \cdots + 7147340761551 \)
T^6 - 276*T^5 - 226899*T^4 - 11197624*T^3 + 3635804355*T^2 + 334047208524*T + 7147340761551
$53$
\( T^{6} + \cdots - 611542622414889 \)
T^6 - 569*T^5 - 201440*T^4 + 96135271*T^3 + 17473333984*T^2 - 3887533444841*T - 611542622414889
$59$
\( T^{6} + 784 T^{5} + \cdots - 32309958702912 \)
T^6 + 784*T^5 + 141444*T^4 - 24574336*T^3 - 10224444496*T^2 - 1021787775744*T - 32309958702912
$61$
\( T^{6} + 28 T^{5} + \cdots - 81331667926737 \)
T^6 + 28*T^5 - 780771*T^4 - 71828152*T^3 + 31684441523*T^2 - 421772851236*T - 81331667926737
$67$
\( T^{6} - 238 T^{5} + \cdots + 11\!\cdots\!72 \)
T^6 - 238*T^5 - 1607168*T^4 + 440109224*T^3 + 598615633408*T^2 - 173358533999584*T + 11538419841377472
$71$
\( T^{6} - 276 T^{5} + \cdots + 23\!\cdots\!04 \)
T^6 - 276*T^5 - 1142628*T^4 + 655525280*T^3 + 111535552752*T^2 - 137064659903808*T + 23010702500119104
$73$
\( T^{6} - 460 T^{5} + \cdots - 25\!\cdots\!97 \)
T^6 - 460*T^5 - 1695235*T^4 + 587899256*T^3 + 601805505875*T^2 - 8210339753068*T - 25558762092914897
$79$
\( T^{6} + 1812 T^{5} + \cdots + 41\!\cdots\!08 \)
T^6 + 1812*T^5 - 249636*T^4 - 1498736672*T^3 - 265685628432*T^2 + 175800409939776*T + 4167617283193408
$83$
\( T^{6} + 87 T^{5} + \cdots - 50\!\cdots\!25 \)
T^6 + 87*T^5 - 2841612*T^4 - 442582965*T^3 + 2286016472124*T^2 + 298366297750215*T - 504105845648410225
$89$
\( T^{6} - 176 T^{5} + \cdots + 23\!\cdots\!84 \)
T^6 - 176*T^5 - 3054140*T^4 - 253054592*T^3 + 2274359296432*T^2 + 934987921726720*T + 23792181603105984
$97$
\( T^{6} + 27 T^{5} + \cdots + 13\!\cdots\!09 \)
T^6 + 27*T^5 - 2043198*T^4 + 43025975*T^3 + 385267189530*T^2 + 45999945343155*T + 1353148357619709
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