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Properties

Label 1560.4.bg
Level $1560$
Weight $4$
Character orbit 1560.bg
Rep. character $\chi_{1560}(601,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $168$
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.bg (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2048 168 1880
Cusp forms 1984 168 1816
Eisenstein series 64 0 64

Trace form

\( 168 q + 12 q^{3} + 36 q^{7} - 756 q^{9} + O(q^{10}) \) \( 168 q + 12 q^{3} + 36 q^{7} - 756 q^{9} + 28 q^{11} + 36 q^{13} - 8 q^{17} - 428 q^{19} - 120 q^{21} + 152 q^{23} + 4200 q^{25} - 216 q^{27} + 280 q^{29} - 256 q^{31} - 260 q^{35} - 504 q^{37} + 828 q^{39} + 888 q^{41} + 1428 q^{43} - 2128 q^{47} - 3692 q^{49} - 240 q^{51} - 2352 q^{53} - 180 q^{55} - 336 q^{57} + 1216 q^{59} + 1140 q^{61} + 324 q^{63} - 420 q^{65} + 492 q^{67} - 1000 q^{71} - 216 q^{73} + 300 q^{75} - 1760 q^{77} - 480 q^{79} - 6804 q^{81} - 2528 q^{83} - 408 q^{87} - 756 q^{89} - 5648 q^{91} + 924 q^{93} - 1068 q^{97} - 504 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)