Properties

Label 2940.2.dg
Level $2940$
Weight $2$
Character orbit 2940.dg
Rep. character $\chi_{2940}(109,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $672$
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.dg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8208 672 7536
Cusp forms 7920 672 7248
Eisenstein series 288 0 288

Trace form

\( 672 q - 2 q^{5} - 56 q^{9} + O(q^{10}) \) \( 672 q - 2 q^{5} - 56 q^{9} + 36 q^{11} + 10 q^{15} + 48 q^{19} + 4 q^{21} - 4 q^{25} - 8 q^{29} - 10 q^{35} - 52 q^{39} + 8 q^{41} - 26 q^{45} - 64 q^{49} + 52 q^{51} - 44 q^{55} - 56 q^{59} + 88 q^{61} + 6 q^{65} + 24 q^{69} + 8 q^{71} + 8 q^{75} + 56 q^{81} - 40 q^{85} + 16 q^{89} + 68 q^{91} + 206 q^{95} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)