Properties

Label 1560.4.gd
Level $1560$
Weight $4$
Character orbit 1560.gd
Rep. character $\chi_{1560}(947,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4000$
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.gd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
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 4064 0
Cusp forms 4000 4000 0
Eisenstein series 64 64 0

Trace form

\( 4000 q - 4 q^{3} - 8 q^{6} + O(q^{10}) \) \( 4000 q - 4 q^{3} - 8 q^{6} + 20 q^{10} - 8 q^{16} + 24 q^{18} - 220 q^{22} - 584 q^{24} - 16 q^{27} - 516 q^{28} - 38 q^{30} - 12 q^{33} + 64 q^{34} - 12 q^{36} - 280 q^{40} - 104 q^{42} - 888 q^{43} - 16 q^{46} + 3772 q^{48} + 93296 q^{49} - 324 q^{52} - 1040 q^{54} + 1300 q^{58} + 136 q^{60} - 16 q^{66} - 24 q^{67} - 2376 q^{70} - 1026 q^{72} - 12 q^{75} + 496 q^{76} + 6464 q^{78} - 8 q^{81} + 1708 q^{82} - 7240 q^{84} + 5188 q^{88} - 1032 q^{90} - 32 q^{91} - 192 q^{94} + 6464 q^{96} - 24 q^{97} - 10624 q^{99} + O(q^{100}) \)

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

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