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Properties

Label 1560.4.ez
Level $1560$
Weight $4$
Character orbit 1560.ez
Rep. character $\chi_{1560}(461,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2688$
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.ez (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
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 2688 1376
Cusp forms 4000 2688 1312
Eisenstein series 64 0 64

Trace form

\( 2688 q + 60 q^{6} + O(q^{10}) \) \( 2688 q + 60 q^{6} + 744 q^{18} + 736 q^{24} - 72 q^{28} - 240 q^{30} - 360 q^{34} - 3060 q^{36} - 680 q^{42} - 1440 q^{46} + 40 q^{48} - 4320 q^{49} - 7344 q^{52} + 1072 q^{54} + 1800 q^{58} + 11160 q^{66} + 8864 q^{72} + 864 q^{73} + 4560 q^{76} - 2532 q^{78} - 6840 q^{82} + 932 q^{84} + 8112 q^{87} + 4680 q^{94} - 7364 q^{96} + 3168 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)