[N,k,chi] = [64,20,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 20);
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} + 23732T_{3}^{2} - 1785165264T_{3} - 7068250797120 \)
T3^3 + 23732*T3^2 - 1785165264*T3 - 7068250797120
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} + 23732 T^{2} + \cdots - 7068250797120 \)
T^3 + 23732*T^2 - 1785165264*T - 7068250797120
$5$
\( T^{3} + 2140218 T^{2} + \cdots - 15\!\cdots\!00 \)
T^3 + 2140218*T^2 - 62490143092980*T - 159302904025585205000
$7$
\( T^{3} - 55851720 T^{2} + \cdots + 24\!\cdots\!88 \)
T^3 - 55851720*T^2 - 35359196993241408*T + 2456350323540529868057088
$11$
\( T^{3} - 297392964 T^{2} + \cdots - 11\!\cdots\!16 \)
T^3 - 297392964*T^2 - 14920813600676267856*T - 11632676765646535843800602816
$13$
\( T^{3} - 14862401022 T^{2} + \cdots - 48\!\cdots\!64 \)
T^3 - 14862401022*T^2 - 3769409476439867325780*T - 48175254424132873544680595285864
$17$
\( T^{3} - 803332464534 T^{2} + \cdots - 13\!\cdots\!00 \)
T^3 - 803332464534*T^2 + 195252528656639248120140*T - 13777558071719191807421638856189000
$19$
\( T^{3} + 3212269666884 T^{2} + \cdots + 59\!\cdots\!96 \)
T^3 + 3212269666884*T^2 + 2755596196957842692743344*T + 593451969118704229673933746080303296
$23$
\( T^{3} - 24948509305560 T^{2} + \cdots - 44\!\cdots\!32 \)
T^3 - 24948509305560*T^2 + 191176629761223002713021632*T - 449026312198759127973838321712739922432
$29$
\( T^{3} + 77667139511058 T^{2} + \cdots - 42\!\cdots\!52 \)
T^3 + 77667139511058*T^2 - 6753081747039043039038692244*T - 42354617027154749334978423238188120019752
$31$
\( T^{3} + 248431735193568 T^{2} + \cdots - 68\!\cdots\!00 \)
T^3 + 248431735193568*T^2 - 24769365747862929695206364160*T - 6870941811522201557070364907873684693811200
$37$
\( T^{3} - 414866302559142 T^{2} + \cdots + 52\!\cdots\!68 \)
T^3 - 414866302559142*T^2 - 270082888937491625167266604404*T + 5282189796660379985901062180632502428424568
$41$
\( T^{3} + \cdots + 41\!\cdots\!44 \)
T^3 - 2818737880869678*T^2 - 1478626127956014413095431952020*T + 4108579764285685848672715616377450287832566744
$43$
\( T^{3} + \cdots + 10\!\cdots\!44 \)
T^3 - 6663230715469860*T^2 + 10702295339112241895166821155248*T + 1083747859654134872602922205890856514691201344
$47$
\( T^{3} + \cdots - 59\!\cdots\!12 \)
T^3 - 1500497644728624*T^2 - 37344275481942278329260753739008*T - 59978125640924807896287874587743861074957504512
$53$
\( T^{3} + \cdots + 21\!\cdots\!32 \)
T^3 + 56067344774978154*T^2 + 836299860177082772015104835031372*T + 2115180385141375518846630056009540011232106824632
$59$
\( T^{3} + \cdots + 11\!\cdots\!76 \)
T^3 - 154317270851496852*T^2 + 3698195724460212627443073336536880*T + 117470837235680569887992721174140201656719083238976
$61$
\( T^{3} + \cdots + 93\!\cdots\!00 \)
T^3 - 134994376571654862*T^2 - 9274999423887262084059006058984980*T + 934304378606410370625884885126789848664402185773400
$67$
\( T^{3} + \cdots - 32\!\cdots\!56 \)
T^3 + 151032181904450292*T^2 - 22023940155653166863011185045854160*T - 3272960762554835529952659557818652418382363771195456
$71$
\( T^{3} + \cdots - 32\!\cdots\!80 \)
T^3 - 1210541848845584136*T^2 + 405511910229834917184133507218504384*T - 32659604177454352844273130352846868789292196139886080
$73$
\( T^{3} + \cdots - 27\!\cdots\!32 \)
T^3 + 81876123599662770*T^2 - 362385451385756586178105289938797588*T - 2799334115820757195756659053920503643136868365707432
$79$
\( T^{3} + \cdots + 34\!\cdots\!80 \)
T^3 - 1439028483035907408*T^2 - 2391119470947012009595086460596251904*T + 3418082622193220133814704086628730014098667520183930880
$83$
\( T^{3} + \cdots + 28\!\cdots\!52 \)
T^3 - 983438102798849916*T^2 - 4559936961842326176173015904088418640*T + 2808654622941535065708842814937669562700048784354626752
$89$
\( T^{3} + \cdots - 55\!\cdots\!16 \)
T^3 + 1312857528832070946*T^2 - 7632401100231002870607889769409443796*T - 5535613902296393718792820933695305942986410551316944616
$97$
\( T^{3} + \cdots - 60\!\cdots\!48 \)
T^3 - 14033245412567998566*T^2 + 57621947782930425325836841784241786252*T - 60436449565999638056521128762198909189458101098806778248
show more
show less