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Properties

Label 560.5.bf
Level $560$
Weight $5$
Character orbit 560.bf
Rep. character $\chi_{560}(69,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $760$
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.bf (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
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 776 776 0
Cusp forms 760 760 0
Eisenstein series 16 16 0

Trace form

\( 760 q - 8 q^{4} + O(q^{10}) \) \( 760 q - 8 q^{4} - 8 q^{11} - 284 q^{14} - 8 q^{15} - 8 q^{16} + 320 q^{21} - 8 q^{29} + 1240 q^{30} + 3840 q^{35} + 11440 q^{36} + 5800 q^{44} - 136 q^{46} - 8 q^{49} + 10696 q^{50} - 656 q^{51} - 9608 q^{56} + 7184 q^{60} + 51160 q^{64} - 8 q^{65} + 10188 q^{70} + 46984 q^{74} - 16 q^{79} - 507400 q^{81} - 59216 q^{84} - 2504 q^{85} + 16 q^{86} + 16896 q^{91} - 50696 q^{95} + 51832 q^{99} + O(q^{100}) \)

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.