Properties

Label 3312.2.dc
Level $3312$
Weight $2$
Character orbit 3312.dc
Rep. character $\chi_{3312}(79,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $2880$
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.dc (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 828 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 11760 2880 8880
Cusp forms 11280 2880 8400
Eisenstein series 480 0 480

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q - 144 q^{25} + 24 q^{29} + 144 q^{49} + 48 q^{69} - 48 q^{77} - 456 q^{81} - 96 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(828, [\chi])\)\(^{\oplus 3}\)