Properties

Label 2340.2.gb
Level $2340$
Weight $2$
Character orbit 2340.gb
Rep. character $\chi_{2340}(691,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1344$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.gb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 468 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

Total New Old
Modular forms 2048 1344 704
Cusp forms 1984 1344 640
Eisenstein series 64 0 64

Trace form

\( 1344 q - 24 q^{6} + 12 q^{8} + O(q^{10}) \) \( 1344 q - 24 q^{6} + 12 q^{8} + 12 q^{18} + 16 q^{24} + 40 q^{26} - 48 q^{30} + 36 q^{36} + 40 q^{42} - 32 q^{44} - 40 q^{48} + 36 q^{52} + 16 q^{54} + 72 q^{58} + 36 q^{62} + 92 q^{66} - 4 q^{72} + 56 q^{74} + 96 q^{77} + 24 q^{78} - 16 q^{80} + 20 q^{84} + 176 q^{86} - 40 q^{92} - 224 q^{93} + 152 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)