Properties

Label 1332.1.bj
Level 13321332
Weight 11
Character orbit 1332.bj
Rep. character χ1332(307,)\chi_{1332}(307,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 44
Newform subspaces 11
Sturm bound 228228
Trace bound 00

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Defining parameters

Level: N N == 1332=223237 1332 = 2^{2} \cdot 3^{2} \cdot 37
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1332.bj (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 148 148
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 1 1
Sturm bound: 228228
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M1(1332,[χ])M_{1}(1332, [\chi]).

Total New Old
Modular forms 20 8 12
Cusp forms 4 4 0
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

DnD_n A4A_4 S4S_4 A5A_5
Dimension 4 0 0 0

Trace form

4q+2q4+4q102q162q34+2q37+2q402q49+2q586q614q64+8q734q85+O(q100) 4 q + 2 q^{4} + 4 q^{10} - 2 q^{16} - 2 q^{34} + 2 q^{37} + 2 q^{40} - 2 q^{49} + 2 q^{58} - 6 q^{61} - 4 q^{64} + 8 q^{73} - 4 q^{85}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(1332,[χ])S_{1}^{\mathrm{new}}(1332, [\chi]) into newform subspaces

Label Char Prim Dim AA Field Image CM RM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
1332.1.bj.a 1332.bj 148.j 44 0.6650.665 Q(ζ12)\Q(\zeta_{12}) D6D_{6} Q(1)\Q(\sqrt{-1}) None 1332.1.bj.a 00 00 00 00 q+ζ125q2ζ124q4ζ12q5+ζ123q8+q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots