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Properties

Label 3240.2.bk
Level $3240$
Weight $2$
Character orbit 3240.bk
Rep. character $\chi_{3240}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.bk (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

\( 568 q + 4 q^{4} + O(q^{10}) \) \( 568 q + 4 q^{4} - 12 q^{10} + 4 q^{16} + 4 q^{25} + 8 q^{31} - 34 q^{34} + 12 q^{40} + 68 q^{46} + 268 q^{49} + 32 q^{55} + 52 q^{64} - 18 q^{70} - 42 q^{76} + 8 q^{79} + 116 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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