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Properties

Label 1560.4.dh
Level $1560$
Weight $4$
Character orbit 1560.dh
Rep. character $\chi_{1560}(589,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1008$
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.dh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2032 1008 1024
Cusp forms 2000 1008 992
Eisenstein series 32 0 32

Trace form

\( 1008 q - 4536 q^{9} + O(q^{10}) \) \( 1008 q - 4536 q^{9} + 36 q^{10} - 208 q^{14} - 128 q^{16} - 88 q^{25} - 224 q^{26} + 204 q^{30} + 952 q^{40} - 1416 q^{41} - 1260 q^{46} - 24696 q^{49} + 516 q^{50} + 144 q^{55} + 692 q^{56} + 1872 q^{64} + 172 q^{65} + 2544 q^{66} + 1168 q^{74} - 8940 q^{76} + 12640 q^{79} - 40824 q^{81} - 648 q^{90} - 344 q^{94} - 1240 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)