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Properties

Label 560.5.ba
Level $560$
Weight $5$
Character orbit 560.ba
Rep. character $\chi_{560}(99,\cdot)$
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.ba (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

\( 576 q + O(q^{10}) \) \( 576 q + 952 q^{16} - 1408 q^{19} + 2604 q^{20} - 3880 q^{24} - 1272 q^{26} + 2048 q^{30} + 4664 q^{34} + 3352 q^{36} + 180 q^{40} + 17640 q^{44} + 9632 q^{46} - 197568 q^{49} + 9576 q^{50} - 8064 q^{51} - 7776 q^{54} - 23552 q^{55} + 10584 q^{56} - 25608 q^{60} + 7552 q^{61} - 10152 q^{64} - 4032 q^{65} + 48808 q^{66} + 19584 q^{69} + 15288 q^{70} + 7128 q^{74} - 27712 q^{75} + 20800 q^{76} + 36300 q^{80} - 419904 q^{81} + 4248 q^{86} - 64336 q^{90} + 45440 q^{94} + 52768 q^{96} + 46592 q^{99} + O(q^{100}) \)

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

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