Properties

Label 296.2.j
Level 296296
Weight 22
Character orbit 296.j
Rep. character χ296(43,)\chi_{296}(43,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 7272
Newform subspaces 22
Sturm bound 7676
Trace bound 11

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 296=2337 296 = 2^{3} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 296.j (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 296 296
Character field: Q(i)\Q(i)
Newform subspaces: 2 2
Sturm bound: 7676
Trace bound: 11
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M2(296,[χ])M_{2}(296, [\chi]).

Total New Old
Modular forms 80 80 0
Cusp forms 72 72 0
Eisenstein series 8 8 0

Trace form

72q4q2+2q64q872q94q10+8q12+10q1424q168q17+14q184q19+4q20+14q22+44q244q264q32+16q3320q34++78q98+O(q100) 72 q - 4 q^{2} + 2 q^{6} - 4 q^{8} - 72 q^{9} - 4 q^{10} + 8 q^{12} + 10 q^{14} - 24 q^{16} - 8 q^{17} + 14 q^{18} - 4 q^{19} + 4 q^{20} + 14 q^{22} + 44 q^{24} - 4 q^{26} - 4 q^{32} + 16 q^{33} - 20 q^{34}+ \cdots + 78 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(296,[χ])S_{2}^{\mathrm{new}}(296, [\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}
296.2.j.a 296.j 296.j 88 2.3642.364 8.0.\cdots.12 None 296.2.j.a 8-8 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+(1+β2)q2+(β2β6)q32β2q4+q+(-1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}-2\beta _{2}q^{4}+\cdots
296.2.j.b 296.j 296.j 6464 2.3642.364 None 296.2.j.b 44 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]