Properties

Label 1560.2.cr
Level $1560$
Weight $2$
Character orbit 1560.cr
Rep. character $\chi_{1560}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.cr (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 576 112
Cusp forms 656 576 80
Eisenstein series 32 0 32

Trace form

\( 576 q + O(q^{10}) \) \( 576 q + 8 q^{10} - 8 q^{16} + 28 q^{18} + 8 q^{22} - 32 q^{28} + 40 q^{30} + 32 q^{31} - 8 q^{40} + 40 q^{42} - 64 q^{46} - 28 q^{48} - 8 q^{52} - 32 q^{58} - 100 q^{60} - 56 q^{66} - 96 q^{70} - 100 q^{72} + 96 q^{76} + 32 q^{81} - 88 q^{82} - 112 q^{87} + 56 q^{88} - 136 q^{90} + 56 q^{96} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)