Properties

Label 3276.2.u
Level 32763276
Weight 22
Character orbit 3276.u
Rep. character χ3276(289,)\chi_{3276}(289,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 9494
Newform subspaces 1313
Sturm bound 13441344
Trace bound 77

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Defining parameters

Level: N N == 3276=2232713 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3276.u (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 91 91
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 13 13
Sturm bound: 13441344
Trace bound: 77
Distinguishing TpT_p: 55, 1111, 1919, 3131

Dimensions

The following table gives the dimensions of various subspaces of M2(3276,[χ])M_{2}(3276, [\chi]).

Total New Old
Modular forms 1392 94 1298
Cusp forms 1296 94 1202
Eisenstein series 96 0 96

Trace form

94q6q1120q177q19+4q2347q25+6q2911q31+10q35+4q37+7q41+2q438q49+11q53+7q55+16q5911q6120q6529q67++14q97+O(q100) 94 q - 6 q^{11} - 20 q^{17} - 7 q^{19} + 4 q^{23} - 47 q^{25} + 6 q^{29} - 11 q^{31} + 10 q^{35} + 4 q^{37} + 7 q^{41} + 2 q^{43} - 8 q^{49} + 11 q^{53} + 7 q^{55} + 16 q^{59} - 11 q^{61} - 20 q^{65} - 29 q^{67}+ \cdots + 14 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(3276,[χ])S_{2}^{\mathrm{new}}(3276, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
3276.2.u.a 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) None 1092.2.r.d 00 00 3-3 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q3ζ6q5+(1+3ζ6)q7+4ζ6q11+q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+4\zeta_{6}q^{11}+\cdots
3276.2.u.b 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) None 1092.2.r.c 00 00 1-1 55 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q5+(3ζ6)q74ζ6q11+(3+)q13+q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}-4\zeta_{6}q^{11}+(-3+\cdots)q^{13}+\cdots
3276.2.u.c 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) 3276.2.u.c 00 00 00 4-4 U(1)[D3]\mathrm{U}(1)[D_{3}] q+(12ζ6)q7+(1+4ζ6)q13+q+(-1-2\zeta_{6})q^{7}+(-1+4\zeta_{6})q^{13}+\cdots
3276.2.u.d 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) 3276.2.u.d 00 00 00 1-1 U(1)[D3]\mathrm{U}(1)[D_{3}] q+(2+3ζ6)q7+(1+3ζ6)q13+(7+)q19+q+(-2+3\zeta_{6})q^{7}+(1+3\zeta_{6})q^{13}+(7+\cdots)q^{19}+\cdots
3276.2.u.e 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) 3276.2.u.e 00 00 00 55 U(1)[D3]\mathrm{U}(1)[D_{3}] q+(2+ζ6)q7+(3ζ6)q13+(1ζ6)q19+q+(2+\zeta_{6})q^{7}+(-3-\zeta_{6})q^{13}+(1-\zeta_{6})q^{19}+\cdots
3276.2.u.f 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) None 1092.2.r.b 00 00 11 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q5+(1+3ζ6)q7+(14ζ6)q13+q+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(1-4\zeta_{6})q^{13}+\cdots
3276.2.u.g 3276.u 91.h 22 26.15926.159 Q(3)\Q(\sqrt{-3}) None 1092.2.r.a 00 00 44 5-5 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+4ζ6q5+(2ζ6)q74ζ6q11+q+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-4\zeta_{6}q^{11}+\cdots
3276.2.u.h 3276.u 91.h 44 26.15926.159 Q(3,13)\Q(\sqrt{-3}, \sqrt{13}) None 3276.2.u.h 00 00 6-6 2-2 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q3β1q5+(13β1)q7+(β1+β2+)q11+q-3\beta _{1}q^{5}+(1-3\beta _{1})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots
3276.2.u.i 3276.u 91.h 44 26.15926.159 Q(3,13)\Q(\sqrt{-3}, \sqrt{13}) None 3276.2.u.h 00 00 66 2-2 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(33β1)q5+(2+3β1)q7+(1+)q11+q+(3-3\beta _{1})q^{5}+(-2+3\beta _{1})q^{7}+(1+\cdots)q^{11}+\cdots
3276.2.u.j 3276.u 91.h 1212 26.15926.159 Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots) None 1092.2.r.e 00 00 4-4 5-5 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1β3+β7β10)q5β2q7+q+(-1-\beta _{3}+\beta _{7}-\beta _{10})q^{5}-\beta _{2}q^{7}+\cdots
3276.2.u.k 3276.u 91.h 1818 26.15926.159 Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots) None 364.2.i.a 00 00 00 44 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β8q5+(β10β13)q7+(β7+)q11+q+\beta _{8}q^{5}+(-\beta _{10}-\beta _{13})q^{7}+(-\beta _{7}+\cdots)q^{11}+\cdots
3276.2.u.l 3276.u 91.h 1818 26.15926.159 Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots) None 1092.2.r.f 00 00 33 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q5β12q7+(β10β17)q11+q+\beta _{1}q^{5}-\beta _{12}q^{7}+(-\beta _{10}-\beta _{17})q^{11}+\cdots
3276.2.u.m 3276.u 91.h 2424 26.15926.159 None 3276.2.u.m 00 00 00 22 SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Decomposition of S2old(3276,[χ])S_{2}^{\mathrm{old}}(3276, [\chi]) into lower level spaces