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Properties

Label 2940.2.cr
Level $2940$
Weight $2$
Character orbit 2940.cr
Rep. character $\chi_{2940}(113,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1344$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.cr (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

Total New Old
Modular forms 8208 1344 6864
Cusp forms 7920 1344 6576
Eisenstein series 288 0 288

Trace form

\( 1344 q + 4 q^{7} + O(q^{10}) \) \( 1344 q + 4 q^{7} + 12 q^{15} - 36 q^{27} - 16 q^{31} - 20 q^{33} + 32 q^{43} - 92 q^{45} + 8 q^{55} + 2 q^{57} - 8 q^{61} - 16 q^{63} + 32 q^{67} - 8 q^{73} + 92 q^{75} - 20 q^{81} - 24 q^{85} - 20 q^{87} + 224 q^{91} + 50 q^{93} + 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)