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Properties

Label 2940.2.bw
Level $2940$
Weight $2$
Character orbit 2940.bw
Rep. character $\chi_{2940}(557,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2880 320 2560
Cusp forms 2496 320 2176
Eisenstein series 384 0 384

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 12 q^{15} + 16 q^{25} + 16 q^{31} - 10 q^{33} + 16 q^{37} - 32 q^{43} + 10 q^{45} + 24 q^{51} + 16 q^{55} - 76 q^{57} + 48 q^{61} + 16 q^{67} + 8 q^{73} + 40 q^{75} + 12 q^{81} + 56 q^{85} + 38 q^{87} + 22 q^{93} + 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)