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Properties

Label 1560.4.e
Level $1560$
Weight $4$
Character orbit 1560.e
Rep. character $\chi_{1560}(131,\cdot)$
Character field $\Q$
Dimension $576$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1560.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1560, [\chi])\).

Total New Old
Modular forms 1016 576 440
Cusp forms 1000 576 424
Eisenstein series 16 0 16

Trace form

\( 576 q + 12 q^{4} + O(q^{10}) \) \( 576 q + 12 q^{4} + 60 q^{10} - 220 q^{12} - 612 q^{16} - 140 q^{18} - 48 q^{19} - 96 q^{22} + 500 q^{24} + 14400 q^{25} + 672 q^{28} - 464 q^{33} - 1272 q^{34} - 700 q^{36} - 420 q^{40} + 3724 q^{42} + 2976 q^{46} + 1032 q^{48} - 28224 q^{49} + 2800 q^{51} - 3564 q^{54} + 688 q^{57} - 3552 q^{58} - 980 q^{60} - 3108 q^{64} + 624 q^{66} - 6528 q^{67} + 1080 q^{70} + 2156 q^{72} + 2808 q^{76} - 1820 q^{78} - 608 q^{81} - 3888 q^{82} - 8876 q^{84} - 9456 q^{88} - 2208 q^{94} + 8504 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)