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Properties

Label 560.5.bh
Level $560$
Weight $5$
Character orbit 560.bh
Rep. character $\chi_{560}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 792 144 648
Cusp forms 744 144 600
Eisenstein series 48 0 48

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 240 q^{13} + 1344 q^{15} + 240 q^{17} - 336 q^{25} + 1920 q^{27} + 256 q^{31} - 2800 q^{37} + 8960 q^{43} + 6480 q^{45} - 14400 q^{47} - 768 q^{51} - 5040 q^{53} + 18048 q^{55} - 3520 q^{57} - 7552 q^{61} + 5328 q^{65} - 26880 q^{67} + 576 q^{71} + 13200 q^{73} + 10688 q^{75} - 104976 q^{81} + 24000 q^{83} + 7280 q^{85} + 66560 q^{87} - 14400 q^{93} + 16704 q^{95} + 9360 q^{97} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)