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Properties

Label 3312.2.br
Level $3312$
Weight $2$
Character orbit 3312.br
Rep. character $\chi_{3312}(965,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2288$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3312.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3312 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3312, [\chi])\).

Total New Old
Modular forms 2320 2320 0
Cusp forms 2288 2288 0
Eisenstein series 32 32 0

Trace form

\( 2288 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 14 q^{6} + O(q^{10}) \) \( 2288 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 14 q^{6} + 4 q^{12} - 4 q^{13} - 4 q^{16} - 8 q^{24} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 12 q^{32} - 18 q^{36} + 24 q^{46} - 24 q^{47} - 20 q^{48} - 1104 q^{49} - 168 q^{50} - 4 q^{52} - 8 q^{54} + 14 q^{58} - 48 q^{59} - 52 q^{64} + 2 q^{69} - 32 q^{70} - 184 q^{72} - 12 q^{77} + 110 q^{78} - 16 q^{81} + 36 q^{82} - 24 q^{85} - 120 q^{92} + 28 q^{93} - 20 q^{94} - 24 q^{95} - 76 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3312, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.