[N,k,chi] = [10,11,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 11);
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\)
\(7\)
\(\chi(n)\)
\(\beta_{1}\)
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 subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - 128T_{3}^{5} + 8192T_{3}^{4} + 20688696T_{3}^{3} + 30028037796T_{3}^{2} - 258527462832T_{3} + 1112900707872 \)
T3^6 - 128*T3^5 + 8192*T3^4 + 20688696*T3^3 + 30028037796*T3^2 - 258527462832*T3 + 1112900707872
acting on \(S_{11}^{\mathrm{new}}(10, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{2} + 32 T + 512)^{3} \)
(T^2 + 32*T + 512)^3
$3$
\( T^{6} - 128 T^{5} + \cdots + 1112900707872 \)
T^6 - 128*T^5 + 8192*T^4 + 20688696*T^3 + 30028037796*T^2 - 258527462832*T + 1112900707872
$5$
\( T^{6} - 5460 T^{5} + \cdots + 93\!\cdots\!25 \)
T^6 - 5460*T^5 - 6416625*T^4 + 85710975000*T^3 - 62662353515625*T^2 - 520706176757812500*T + 931322574615478515625
$7$
\( T^{6} - 13512 T^{5} + \cdots + 13\!\cdots\!12 \)
T^6 - 13512*T^5 + 91287072*T^4 + 9497368375544*T^3 + 335503136731458276*T^2 + 967807407319475146032*T + 1395890343660414229255712
$11$
\( (T^{3} - 323916 T^{2} + \cdots + 26\!\cdots\!52)^{2} \)
(T^3 - 323916*T^2 + 9059018052*T + 2666505072779552)^2
$13$
\( T^{6} + 742902 T^{5} + \cdots + 77\!\cdots\!52 \)
T^6 + 742902*T^5 + 275951690802*T^4 + 2391666107193216*T^3 + 26912797686745338345156*T^2 + 20385926932644041898677185368*T + 7720973897629741929756764276014152
$17$
\( T^{6} + 755118 T^{5} + \cdots + 28\!\cdots\!32 \)
T^6 + 755118*T^5 + 285101596962*T^4 + 702350500374552064*T^3 + 5096187989047266077846916*T^2 + 5433761139804361512989169352632*T + 2896847622959042762767646245377431432
$19$
\( T^{6} + 619530339600 T^{4} + \cdots + 20\!\cdots\!00 \)
T^6 + 619530339600*T^4 + 75294310961554272000000*T^2 + 2056723660260006210847360000000000
$23$
\( T^{6} + 15052992 T^{5} + \cdots + 71\!\cdots\!92 \)
T^6 + 15052992*T^5 + 113296284076032*T^4 + 291518088619178721976*T^3 + 130974622332119758626480036*T^2 - 1364693886574721220928404130560432*T + 7109733820540638431039885244948460162592
$29$
\( T^{6} + \cdots + 13\!\cdots\!00 \)
T^6 + 1890131069150400*T^4 + 783357884027284635512471040000*T^2 + 1396665752624284439971199690308489216000000
$31$
\( (T^{3} - 76923576 T^{2} + \cdots - 10\!\cdots\!88)^{2} \)
(T^3 - 76923576*T^2 + 1721402358911892*T - 10349511565794772049488)^2
$37$
\( T^{6} + 32574498 T^{5} + \cdots + 28\!\cdots\!52 \)
T^6 + 32574498*T^5 + 530548959976002*T^4 - 192244675901723344874016*T^3 + 12904798909133020317138403686756*T^2 - 270238009196569101743796081290830347768*T + 2829512576241733403460259217277933867662734152
$41$
\( (T^{3} - 113076636 T^{2} + \cdots + 19\!\cdots\!72)^{2} \)
(T^3 - 113076636*T^2 - 17656457682251868*T + 1969427592056349349290272)^2
$43$
\( T^{6} + 63628752 T^{5} + \cdots + 31\!\cdots\!52 \)
T^6 + 63628752*T^5 + 2024309040538752*T^4 - 208408650620129539725384*T^3 + 248590065656793906058321152184356*T^2 + 12531550791652921131133859302152923668368*T + 315860903026969162616545479464449517690718526752
$47$
\( T^{6} + 19700448 T^{5} + \cdots + 89\!\cdots\!52 \)
T^6 + 19700448*T^5 + 194053825700352*T^4 - 5148803150521107619590216*T^3 + 2214982118121624009700226985928356*T^2 - 198685054037663130935933353211209820862768*T + 8911076612082499140165454300745626514323009361952
$53$
\( T^{6} + 950001042 T^{5} + \cdots + 85\!\cdots\!92 \)
T^6 + 950001042*T^5 + 451250989900542882*T^4 + 101246418608699306815767776*T^3 + 12307635453920678214258295944043236*T^2 + 460010794967834607238463806753857463572168*T + 8596693177954398783181953052938443397014342145992
$59$
\( T^{6} + \cdots + 23\!\cdots\!00 \)
T^6 + 1405683550765923600*T^4 + 493419938447922297487605409693440000*T^2 + 2335042254732478561687629855191624121156649984000000
$61$
\( (T^{3} - 801992196 T^{2} + \cdots + 15\!\cdots\!32)^{2} \)
(T^3 - 801992196*T^2 - 145162927997988828*T + 159337479955441782276666432)^2
$67$
\( T^{6} - 2502647712 T^{5} + \cdots + 29\!\cdots\!12 \)
T^6 - 2502647712*T^5 + 3131622785189417472*T^4 - 431137369274023583615070856*T^3 + 639820634505338611383803660585802276*T^2 - 1946107207087863339927902902545599877561179568*T + 2959683587266145451389324930077729871536151946614868512
$71$
\( (T^{3} + 3568766904 T^{2} + \cdots + 58\!\cdots\!32)^{2} \)
(T^3 + 3568766904*T^2 + 2731430976824954772*T + 587751485374237526092302832)^2
$73$
\( T^{6} - 2304462438 T^{5} + \cdots + 16\!\cdots\!12 \)
T^6 - 2304462438*T^5 + 2655273564076451922*T^4 - 545627643508260974444723744*T^3 + 294948789716269124536487258280925476*T^2 - 976024349523794434530493863689104510309953432*T + 1614896490641202554796754754181385595349924049232911112
$79$
\( T^{6} + \cdots + 28\!\cdots\!00 \)
T^6 + 3556319314037606400*T^4 + 2090348062530013097709642376151040000*T^2 + 289986691628090502655547883065742261080247238656000000
$83$
\( T^{6} + 88180632 T^{5} + \cdots + 13\!\cdots\!32 \)
T^6 + 88180632*T^5 + 3887911929959712*T^4 - 17583449498157756202276992264*T^3 + 145909315745957370116784515315889631716*T^2 - 199529260116913141866583905543923732515775402832*T + 136426949298149363364809482239358964625391462482980147232
$89$
\( T^{6} + \cdots + 26\!\cdots\!00 \)
T^6 + 74722446831800851200*T^4 + 937590694761194981338758236641812480000*T^2 + 2677712409875171881284867897640404726726156060196864000000
$97$
\( T^{6} - 33281088582 T^{5} + \cdots + 11\!\cdots\!32 \)
T^6 - 33281088582*T^5 + 553815428601465385362*T^4 - 3228364709295081604017665557536*T^3 + 2663272114820993614626635743691360110116*T^2 + 77969299144772454431170854215292292782586667993832*T + 1141305008845409768137530083251420004343340000441747147047432
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