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Properties

Label 2940.2.dm
Level $2940$
Weight $2$
Character orbit 2940.dm
Rep. character $\chi_{2940}(53,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $2688$
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.dm (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16416 2688 13728
Cusp forms 15840 2688 13152
Eisenstein series 576 0 576

Trace form

\( 2688 q - 4 q^{7} + O(q^{10}) \) \( 2688 q - 4 q^{7} - 12 q^{15} - 12 q^{21} + 16 q^{31} - 10 q^{33} - 32 q^{43} + 122 q^{45} + 16 q^{55} - 2 q^{57} - 64 q^{61} - 26 q^{63} + 16 q^{67} + 8 q^{73} - 44 q^{75} + 32 q^{81} + 24 q^{85} + 38 q^{87} - 152 q^{91} + 424 q^{93} + 40 q^{97} + O(q^{100}) \)

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

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