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Properties

Label 1320.2.j
Level $1320$
Weight $2$
Character orbit 1320.j
Rep. character $\chi_{1320}(1189,\cdot)$
Character field $\Q$
Dimension $120$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
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 296 120 176
Cusp forms 280 120 160
Eisenstein series 16 0 16

Trace form

\( 120 q - 4 q^{4} + 4 q^{6} + 120 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{4} + 4 q^{6} + 120 q^{9} + 12 q^{10} + 32 q^{14} + 4 q^{16} - 12 q^{20} + 4 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{30} + 64 q^{31} - 40 q^{34} - 4 q^{36} - 4 q^{40} + 16 q^{41} + 8 q^{44} - 40 q^{46} - 120 q^{49} + 48 q^{50} + 4 q^{54} - 64 q^{56} + 32 q^{60} - 4 q^{64} + 48 q^{65} - 32 q^{70} - 32 q^{71} - 32 q^{74} - 8 q^{76} + 16 q^{79} + 28 q^{80} + 120 q^{81} + 32 q^{84} - 80 q^{86} + 80 q^{89} + 12 q^{90} + 72 q^{94} - 48 q^{95} + 84 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)