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Properties

Label 1560.4.fn
Level $1560$
Weight $4$
Character orbit 1560.fn
Rep. character $\chi_{1560}(89,\cdot)$
Character field $\Q(\zeta_{12})$
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.fn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4096 1008 3088
Cusp forms 3968 1008 2960
Eisenstein series 128 0 128

Trace form

\( 1008 q + O(q^{10}) \) \( 1008 q - 88 q^{15} + 216 q^{31} - 424 q^{39} - 228 q^{45} + 936 q^{55} + 1872 q^{61} - 4260 q^{75} + 1872 q^{79} - 272 q^{81} - 1128 q^{85} - 288 q^{91} - 3728 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)