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Properties

Label 560.5.s
Level $560$
Weight $5$
Character orbit 560.s
Rep. character $\chi_{560}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 776 576 200
Cusp forms 760 576 184
Eisenstein series 16 0 16

Trace form

\( 576 q + 56 q^{4} - 15552 q^{9} + O(q^{10}) \) \( 576 q + 56 q^{4} - 15552 q^{9} - 720 q^{12} - 952 q^{16} + 980 q^{18} + 1408 q^{19} + 1540 q^{22} - 4128 q^{26} + 1844 q^{30} - 5400 q^{32} - 2144 q^{34} - 6048 q^{36} - 840 q^{38} - 6144 q^{40} - 4900 q^{42} + 17920 q^{43} - 4104 q^{44} + 9632 q^{46} - 2760 q^{48} - 14616 q^{50} + 8064 q^{51} - 13520 q^{52} - 4576 q^{54} - 10584 q^{56} - 11580 q^{58} - 26064 q^{60} - 7552 q^{61} - 9000 q^{62} - 2464 q^{64} - 15392 q^{66} - 21120 q^{68} - 19584 q^{69} + 33400 q^{72} + 10560 q^{73} + 4704 q^{74} - 27712 q^{75} + 6656 q^{76} + 36220 q^{78} - 52296 q^{80} + 419904 q^{81} + 15400 q^{82} - 27552 q^{86} - 25720 q^{88} + 12944 q^{90} + 33600 q^{92} + 26296 q^{94} + 52768 q^{96} - 46592 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{5}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)