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Properties

Label 560.3.ck
Level $560$
Weight $3$
Character orbit 560.ck
Rep. character $\chi_{560}(177,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $184$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 560.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(560, [\chi])\).

Total New Old
Modular forms 816 200 616
Cusp forms 720 184 536
Eisenstein series 96 16 80

Trace form

\( 184 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 184 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} + 8 q^{15} - 2 q^{17} - 24 q^{21} - 46 q^{23} - 2 q^{25} + 44 q^{27} + 4 q^{31} - 14 q^{33} + 52 q^{35} - 2 q^{37} - 48 q^{41} + 8 q^{43} - 102 q^{45} + 98 q^{47} - 188 q^{51} - 2 q^{53} - 92 q^{55} - 108 q^{57} - 4 q^{61} + 228 q^{63} - 98 q^{65} - 142 q^{67} - 304 q^{71} - 226 q^{73} + 2 q^{75} + 94 q^{77} + 520 q^{81} - 376 q^{83} - 8 q^{85} - 16 q^{87} + 584 q^{91} + 130 q^{93} + 198 q^{95} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)