↑

Properties

Label 2940.2.bi
Level $2940$
Weight $2$
Character orbit 2940.bi
Rep. character $\chi_{2940}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 320 1088
Cusp forms 1280 320 960
Eisenstein series 128 0 128

Trace form

\( 320 q + 8 q^{2} - 8 q^{4} - 16 q^{8} - 160 q^{9} + O(q^{10}) \) \( 320 q + 8 q^{2} - 8 q^{4} - 16 q^{8} - 160 q^{9} - 16 q^{16} + 8 q^{18} - 24 q^{22} + 36 q^{24} + 160 q^{25} + 60 q^{26} - 128 q^{29} + 28 q^{32} + 16 q^{36} + 56 q^{37} + 8 q^{44} + 20 q^{46} + 16 q^{50} - 36 q^{52} - 48 q^{53} + 48 q^{57} + 12 q^{58} + 48 q^{61} + 16 q^{64} + 8 q^{65} - 36 q^{66} + 60 q^{68} + 8 q^{72} - 72 q^{73} - 16 q^{74} + 24 q^{78} - 160 q^{81} + 12 q^{82} - 148 q^{86} + 136 q^{88} + 296 q^{92} + 8 q^{93} - 36 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)