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Properties

Label 560.5.cs
Level $560$
Weight $5$
Character orbit 560.cs
Rep. character $\chi_{560}(179,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1520$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 560.cs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

Total New Old
Modular forms 1552 1552 0
Cusp forms 1520 1520 0
Eisenstein series 32 32 0

Trace form

\( 1520 q - 4 q^{4} - 2 q^{5} - 16 q^{6} + O(q^{10}) \) \( 1520 q - 4 q^{4} - 2 q^{5} - 16 q^{6} + 196 q^{10} - 4 q^{11} + 360 q^{14} - 4 q^{16} - 4 q^{19} - 8 q^{20} - 332 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 1146 q^{30} - 13904 q^{34} - 3846 q^{35} - 20864 q^{36} - 8 q^{39} - 8526 q^{40} + 2900 q^{44} - 2664 q^{45} - 132 q^{46} - 16 q^{49} + 10820 q^{50} - 652 q^{51} + 2184 q^{54} - 16 q^{55} + 19200 q^{56} + 6524 q^{59} - 7262 q^{60} - 4 q^{61} - 8536 q^{64} - 4 q^{65} + 8724 q^{66} - 664 q^{69} + 13092 q^{70} - 39968 q^{71} - 19936 q^{74} + 322 q^{75} - 76216 q^{76} + 47344 q^{80} + 507376 q^{81} - 78428 q^{84} - 2508 q^{85} + 15884 q^{86} - 15884 q^{90} + 26496 q^{91} + 124 q^{94} - 91876 q^{96} - 53152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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