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Properties

Label 3312.2.bq
Level $3312$
Weight $2$
Character orbit 3312.bq
Rep. character $\chi_{3312}(875,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2112$
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.bq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
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 2112 208
Cusp forms 2288 2112 176
Eisenstein series 32 0 32

Trace form

\( 2112 q - 6 q^{6} + O(q^{10}) \) \( 2112 q - 6 q^{6} + 12 q^{12} + 20 q^{18} + 84 q^{20} - 8 q^{24} + 12 q^{27} + 68 q^{30} + 34 q^{36} + 24 q^{39} - 40 q^{42} - 1056 q^{49} + 40 q^{51} + 68 q^{54} - 18 q^{58} + 36 q^{59} - 164 q^{60} + 36 q^{64} - 184 q^{66} + 60 q^{72} + 112 q^{75} + 70 q^{78} + 36 q^{82} - 120 q^{83} - 296 q^{84} - 120 q^{86} - 112 q^{87} - 48 q^{88} - 12 q^{90} + 24 q^{93} + 176 q^{96} - 64 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)