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Properties

Label 560.5.cd
Level $560$
Weight $5$
Character orbit 560.cd
Rep. character $\chi_{560}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
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.cd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 792 128 664
Cusp forms 744 128 616
Eisenstein series 48 0 48

Trace form

\( 128 q + 1728 q^{9} + O(q^{10}) \) \( 128 q + 1728 q^{9} + 704 q^{13} + 1488 q^{21} - 8000 q^{25} - 3168 q^{29} + 2080 q^{37} - 3744 q^{41} + 1200 q^{45} - 10432 q^{49} - 4896 q^{53} + 7488 q^{57} + 28960 q^{61} + 3600 q^{65} - 13248 q^{69} + 3680 q^{73} + 80928 q^{77} - 42864 q^{81} - 16272 q^{89} - 21408 q^{93} + 896 q^{97} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)