Properties

Label 1560.4.cq
Level $1560$
Weight $4$
Character orbit 1560.cq
Rep. character $\chi_{1560}(547,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $864$
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.cq (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1560, [\chi])\).

Total New Old
Modular forms 2032 864 1168
Cusp forms 2000 864 1136
Eisenstein series 32 0 32

Trace form

\( 864 q - 24 q^{6} - 168 q^{8} + O(q^{10}) \) \( 864 q - 24 q^{6} - 168 q^{8} + 72 q^{10} - 24 q^{12} + 264 q^{16} + 216 q^{22} + 2136 q^{28} - 408 q^{30} - 1824 q^{35} + 216 q^{36} + 80 q^{38} - 648 q^{40} - 864 q^{43} + 4512 q^{46} - 1056 q^{48} + 2976 q^{51} - 936 q^{52} - 672 q^{56} + 728 q^{58} - 2736 q^{66} - 7392 q^{67} + 2928 q^{68} - 1656 q^{70} + 1512 q^{72} + 3744 q^{76} + 6320 q^{80} - 69984 q^{81} + 8288 q^{82} + 7968 q^{86} - 80 q^{88} - 216 q^{90} - 3440 q^{92} - 7656 q^{96} - 2976 q^{97} - 4288 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)