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Properties

Label 1320.2.bf
Level $1320$
Weight $2$
Character orbit 1320.bf
Rep. character $\chi_{1320}(419,\cdot)$
Character field $\Q$
Dimension $240$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.bf (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

Total New Old
Modular forms 296 240 56
Cusp forms 280 240 40
Eisenstein series 16 0 16

Trace form

\( 240 q - 4 q^{4} + O(q^{10}) \) \( 240 q - 4 q^{4} + 4 q^{16} + 16 q^{19} + 28 q^{24} - 34 q^{30} - 8 q^{34} + 40 q^{36} - 36 q^{40} - 72 q^{46} + 240 q^{49} - 52 q^{54} - 20 q^{60} - 52 q^{64} + 56 q^{70} - 56 q^{75} - 128 q^{76} + 16 q^{81} - 40 q^{84} + 78 q^{90} - 48 q^{94} - 36 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)