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Properties

Label 1560.4.cr
Level $1560$
Weight $4$
Character orbit 1560.cr
Rep. character $\chi_{1560}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1728$
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.cr (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
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 1728 304
Cusp forms 2000 1728 272
Eisenstein series 32 0 32

Trace form

\( 1728 q + O(q^{10}) \) \( 1728 q - 72 q^{10} - 264 q^{16} - 476 q^{18} + 216 q^{22} + 864 q^{28} - 1160 q^{30} + 1056 q^{31} - 648 q^{40} + 280 q^{42} - 1152 q^{46} - 2044 q^{48} - 936 q^{52} - 2016 q^{58} + 1100 q^{60} + 952 q^{66} + 6624 q^{70} - 2500 q^{72} + 2208 q^{76} - 2464 q^{81} + 4824 q^{82} + 2576 q^{87} - 4872 q^{88} + 4904 q^{90} + 4088 q^{96} + 2976 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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