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Properties

Label 560.5.cw
Level $560$
Weight $5$
Character orbit 560.cw
Rep. character $\chi_{560}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
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.cw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
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 1584 384 1200
Cusp forms 1488 384 1104
Eisenstein series 96 0 96

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 1824 q^{21} - 12960 q^{33} + 21120 q^{57} + 27072 q^{65} + 7200 q^{77} + 147552 q^{81} + 38592 q^{85} + 43200 q^{93} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)