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Properties

Label 560.5.bo
Level $560$
Weight $5$
Character orbit 560.bo
Rep. character $\chi_{560}(477,\cdot)$
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.bo (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

\( 576 q - 56 q^{4} + 15552 q^{9} + O(q^{10}) \) \( 576 q - 56 q^{4} + 15552 q^{9} - 720 q^{12} - 952 q^{16} - 980 q^{18} - 1408 q^{19} - 2660 q^{22} - 4128 q^{26} + 1844 q^{30} + 1200 q^{32} + 2144 q^{34} - 6048 q^{36} - 840 q^{38} + 5784 q^{40} + 4900 q^{42} + 4104 q^{44} + 9632 q^{46} + 12640 q^{48} + 5376 q^{50} + 8064 q^{51} - 13520 q^{52} + 4576 q^{54} - 10584 q^{56} + 11580 q^{58} + 25624 q^{60} - 7552 q^{61} + 9000 q^{62} + 2464 q^{64} - 15392 q^{66} + 30360 q^{68} + 19584 q^{69} + 46400 q^{72} - 10560 q^{73} - 4704 q^{74} - 32320 q^{75} + 6656 q^{76} - 3820 q^{78} - 45744 q^{80} + 419904 q^{81} - 52600 q^{82} + 48000 q^{83} - 27552 q^{86} + 3320 q^{88} - 90824 q^{90} - 113400 q^{92} - 26296 q^{94} + 52768 q^{96} + 46592 q^{99} + O(q^{100}) \)

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

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