Properties

Label 1560.4.bv
Level $1560$
Weight $4$
Character orbit 1560.bv
Rep. character $\chi_{1560}(883,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1008$
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.bv (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
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 1008 1024
Cusp forms 2000 1008 992
Eisenstein series 32 0 32

Trace form

\( 1008 q + O(q^{10}) \) \( 1008 q + 72 q^{10} - 24 q^{12} - 224 q^{16} + 208 q^{17} + 304 q^{22} - 176 q^{25} + 368 q^{26} - 408 q^{30} + 728 q^{40} + 1320 q^{42} - 864 q^{43} + 1488 q^{52} + 3616 q^{56} + 3344 q^{62} - 1048 q^{65} - 72 q^{78} - 81648 q^{81} - 1824 q^{82} - 2280 q^{88} + 3392 q^{91} - 13424 q^{92} + O(q^{100}) \)

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

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