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Properties

Label 1560.4.ff
Level $1560$
Weight $4$
Character orbit 1560.ff
Rep. character $\chi_{1560}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2016$
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.ff (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4064 2016 2048
Cusp forms 4000 2016 1984
Eisenstein series 64 0 64

Trace form

\( 2016 q + 9072 q^{9} + O(q^{10}) \) \( 2016 q + 9072 q^{9} - 416 q^{14} - 144 q^{16} - 380 q^{20} - 1504 q^{34} - 2856 q^{40} + 1888 q^{41} - 1232 q^{44} - 1680 q^{46} + 2108 q^{50} - 6696 q^{56} + 2752 q^{59} - 2064 q^{60} + 2096 q^{65} + 5088 q^{66} + 408 q^{70} - 8104 q^{76} + 1476 q^{80} - 81648 q^{81} + 7680 q^{86} - 880 q^{89} - 6784 q^{91} + 1520 q^{94} + 5160 q^{96} + O(q^{100}) \)

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

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