Properties

Label 1560.2.x
Level $1560$
Weight $2$
Character orbit 1560.x
Rep. character $\chi_{1560}(1379,\cdot)$
Character field $\Q$
Dimension $288$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.x (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 344 288 56
Cusp forms 328 288 40
Eisenstein series 16 0 16

Trace form

\( 288 q - 4 q^{4} + O(q^{10}) \) \( 288 q - 4 q^{4} - 4 q^{10} + 12 q^{16} + 16 q^{19} + 28 q^{24} - 34 q^{30} - 8 q^{34} + 40 q^{36} - 12 q^{40} - 32 q^{46} + 288 q^{49} + 28 q^{54} - 24 q^{60} - 4 q^{64} - 88 q^{66} + 64 q^{70} - 56 q^{75} - 152 q^{76} + 16 q^{81} - 28 q^{84} + 22 q^{90} + 32 q^{94} - 104 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)