↑

Properties

Label 2940.2.ba
Level $2940$
Weight $2$
Character orbit 2940.ba
Rep. character $\chi_{2940}(1439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $928$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
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 992 416
Cusp forms 1280 928 352
Eisenstein series 128 64 64

Trace form

\( 928 q + 4 q^{4} + 16 q^{6} + 4 q^{9} + O(q^{10}) \) \( 928 q + 4 q^{4} + 16 q^{6} + 4 q^{9} - 6 q^{10} + 4 q^{16} - 4 q^{24} + 26 q^{30} + 32 q^{34} + 48 q^{36} + 18 q^{40} + 22 q^{45} - 8 q^{46} + 12 q^{54} - 6 q^{60} + 8 q^{61} + 40 q^{64} - 16 q^{66} + 56 q^{69} + 192 q^{76} + 16 q^{81} - 40 q^{85} - 104 q^{90} + 8 q^{94} + 64 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)