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Properties

Label 560.4.ci
Level $560$
Weight $4$
Character orbit 560.ci
Rep. character $\chi_{560}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $280$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(560, [\chi])\).

Total New Old
Modular forms 1200 296 904
Cusp forms 1104 280 824
Eisenstein series 96 16 80

Trace form

\( 280 q + 6 q^{3} - 6 q^{5} + 4 q^{7} + O(q^{10}) \) \( 280 q + 6 q^{3} - 6 q^{5} + 4 q^{7} + 4 q^{11} + 8 q^{15} - 6 q^{17} + 128 q^{21} - 82 q^{23} - 2 q^{25} + 12 q^{31} - 78 q^{33} - 224 q^{35} - 2 q^{37} + 8 q^{43} - 6 q^{45} - 606 q^{47} - 308 q^{51} - 2 q^{53} + 1796 q^{57} - 12 q^{61} - 948 q^{63} - 466 q^{65} - 922 q^{67} + 3744 q^{71} - 6 q^{73} + 6 q^{75} + 682 q^{77} + 8128 q^{81} - 8 q^{85} - 156 q^{87} - 1736 q^{91} + 802 q^{93} - 534 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

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