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Properties

Label 1560.2.ez
Level $1560$
Weight $2$
Character orbit 1560.ez
Rep. character $\chi_{1560}(461,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $896$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.ez (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 1376 896 480
Cusp forms 1312 896 416
Eisenstein series 64 0 64

Trace form

\( 896 q - 12 q^{6} + O(q^{10}) \) \( 896 q - 12 q^{6} + 24 q^{18} - 32 q^{24} + 24 q^{28} + 48 q^{30} - 24 q^{34} - 36 q^{36} + 40 q^{42} + 32 q^{46} + 40 q^{48} + 96 q^{49} + 144 q^{52} + 16 q^{54} - 8 q^{58} - 24 q^{66} - 160 q^{72} + 32 q^{73} - 112 q^{76} - 12 q^{78} + 120 q^{82} - 76 q^{84} + 48 q^{87} + 24 q^{94} - 164 q^{96} + 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

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