Properties

Label 3240.2.bd
Level $3240$
Weight $2$
Character orbit 3240.bd
Rep. character $\chi_{3240}(539,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
Sturm bound $1296$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).

Total New Old
Modular forms 1344 584 760
Cusp forms 1248 568 680
Eisenstein series 96 16 80

Trace form

\( 568 q + 4 q^{4} + O(q^{10}) \) \( 568 q + 4 q^{4} + 4 q^{10} + 4 q^{16} - 16 q^{19} + 4 q^{25} - 18 q^{34} - 8 q^{40} - 52 q^{46} - 252 q^{49} - 68 q^{64} + 30 q^{70} + 50 q^{76} - 128 q^{91} - 124 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)