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Properties

Label 1560.2.eh
Level $1560$
Weight $2$
Character orbit 1560.eh
Rep. character $\chi_{1560}(1069,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $336$
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.eh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 336 352
Cusp forms 656 336 320
Eisenstein series 32 0 32

Trace form

\( 336 q - 168 q^{9} + O(q^{10}) \) \( 336 q - 168 q^{9} + 4 q^{10} + 16 q^{14} - 16 q^{16} + 20 q^{20} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 32 q^{34} - 48 q^{40} - 8 q^{41} + 16 q^{44} + 20 q^{46} + 168 q^{49} - 8 q^{50} + 16 q^{55} + 52 q^{56} - 16 q^{60} + 48 q^{64} + 12 q^{65} + 16 q^{66} - 64 q^{70} - 64 q^{71} + 16 q^{74} - 12 q^{76} + 160 q^{79} + 36 q^{80} - 168 q^{81} + 80 q^{89} - 8 q^{90} - 8 q^{94} + 40 q^{95} + 40 q^{96} + O(q^{100}) \)

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

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