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Properties

Label 1560.2.q
Level $1560$
Weight $2$
Character orbit 1560.q
Rep. character $\chi_{1560}(181,\cdot)$
Character field $\Q$
Dimension $112$
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.q (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 344 112 232
Cusp forms 328 112 216
Eisenstein series 16 0 16

Trace form

\( 112 q - 112 q^{9} + O(q^{10}) \) \( 112 q - 112 q^{9} - 16 q^{14} - 16 q^{16} + 24 q^{22} + 112 q^{25} + 12 q^{26} - 80 q^{38} + 24 q^{42} + 32 q^{48} - 80 q^{49} + 48 q^{52} - 32 q^{55} - 24 q^{56} + 64 q^{62} - 32 q^{66} + 16 q^{68} + 32 q^{74} + 32 q^{78} + 112 q^{81} - 104 q^{82} - 48 q^{87} + 32 q^{88} + 48 q^{92} - 128 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)