Properties

Label 3040.2.de
Level $3040$
Weight $2$
Character orbit 3040.de
Rep. character $\chi_{3040}(543,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3040.de (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

Total New Old
Modular forms 1984 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 16 q^{41} - 32 q^{57} - 64 q^{65} + 96 q^{77} + 240 q^{81} - 48 q^{85} - 64 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1520, [\chi])\)\(^{\oplus 2}\)