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Properties

Label 3240.2.m
Level $3240$
Weight $2$
Character orbit 3240.m
Rep. character $\chi_{3240}(1619,\cdot)$
Character field $\Q$
Dimension $280$
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.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 672 296 376
Cusp forms 624 280 344
Eisenstein series 48 16 32

Trace form

\( 280 q + 4 q^{4} + O(q^{10}) \) \( 280 q + 4 q^{4} - 8 q^{10} + 4 q^{16} - 16 q^{19} + 4 q^{25} + 24 q^{34} - 8 q^{40} - 28 q^{46} + 240 q^{49} - 20 q^{64} - 36 q^{70} + 80 q^{76} + 40 q^{91} + 68 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)