↑

Properties

Label 560.3.bg
Level $560$
Weight $3$
Character orbit 560.bg
Rep. character $\chi_{560}(211,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $288$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 560.bg (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(560, [\chi])\).

Total New Old
Modular forms 392 192 200
Cusp forms 376 192 184
Eisenstein series 16 0 16

Trace form

\( 192 q - 12 q^{4} - 24 q^{6} + O(q^{10}) \) \( 192 q - 12 q^{4} - 24 q^{6} + 40 q^{10} - 32 q^{11} + 120 q^{12} + 28 q^{14} - 76 q^{16} - 60 q^{18} + 64 q^{19} + 36 q^{22} + 128 q^{23} - 40 q^{24} + 96 q^{26} + 192 q^{27} - 32 q^{29} - 40 q^{32} - 32 q^{34} + 168 q^{36} + 96 q^{37} - 768 q^{39} - 96 q^{43} - 52 q^{44} + 288 q^{46} + 1344 q^{49} - 20 q^{50} + 192 q^{51} - 320 q^{52} + 160 q^{53} + 288 q^{54} + 28 q^{56} + 100 q^{58} + 576 q^{59} + 64 q^{61} - 312 q^{62} - 468 q^{64} + 416 q^{66} - 160 q^{67} - 552 q^{68} - 192 q^{69} - 892 q^{72} - 396 q^{74} - 1024 q^{76} - 224 q^{77} + 1136 q^{78} + 480 q^{80} - 1728 q^{81} + 392 q^{82} - 320 q^{85} + 708 q^{86} + 300 q^{88} - 432 q^{92} - 192 q^{93} - 280 q^{94} + 176 q^{96} - 736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)