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Properties

Label 3312.2.v
Level $3312$
Weight $2$
Character orbit 3312.v
Rep. character $\chi_{3312}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $352$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1168 352 816
Cusp forms 1136 352 784
Eisenstein series 32 0 32

Trace form

\( 352 q + O(q^{10}) \) \( 352 q + 80 q^{22} + 48 q^{28} + 64 q^{43} + 352 q^{49} + 16 q^{52} + 128 q^{55} + 96 q^{64} + 144 q^{70} + 48 q^{76} - 80 q^{82} - 112 q^{88} - 96 q^{91} + 48 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)