Properties

Label 1560.4.ft
Level $1560$
Weight $4$
Character orbit 1560.ft
Rep. character $\chi_{1560}(113,\cdot)$
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.ft (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

\( 1008 q + O(q^{10}) \) \( 1008 q - 24 q^{13} + 552 q^{27} - 432 q^{31} + 204 q^{33} + 792 q^{37} - 624 q^{51} - 936 q^{55} + 2544 q^{57} + 1064 q^{63} + 1944 q^{67} - 720 q^{73} + 1452 q^{75} - 272 q^{81} + 7536 q^{85} - 192 q^{91} + 1956 q^{93} - 2112 q^{97} + O(q^{100}) \)

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

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