Properties

Label 560.5.bt
Level $560$
Weight $5$
Character orbit 560.bt
Rep. character $\chi_{560}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 792 192 600
Cusp forms 744 192 552
Eisenstein series 48 0 48

Trace form

\( 192 q - 2592 q^{9} + O(q^{10}) \) \( 192 q - 2592 q^{9} - 912 q^{21} + 1104 q^{25} - 3168 q^{29} + 3744 q^{41} - 9408 q^{49} - 13536 q^{65} - 38976 q^{69} - 103536 q^{81} + 3360 q^{85} - 16272 q^{89} + O(q^{100}) \)

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

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