↑

Properties

Label 570.4.bb
Level $570$
Weight $4$
Character orbit 570.bb
Rep. character $\chi_{570}(41,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(570, [\chi])\).

Total New Old
Modular forms 2208 480 1728
Cusp forms 2112 480 1632
Eisenstein series 96 0 96

Trace form

\( 480 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + O(q^{10}) \) \( 480 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + 564 q^{13} - 1164 q^{19} - 432 q^{22} - 240 q^{24} + 1314 q^{27} + 1104 q^{28} - 690 q^{33} - 720 q^{34} - 120 q^{36} - 696 q^{39} - 924 q^{43} - 192 q^{48} - 11760 q^{49} + 1410 q^{51} + 2208 q^{52} + 3600 q^{54} + 4416 q^{57} + 2592 q^{58} + 6648 q^{61} + 1344 q^{63} - 15360 q^{64} - 1500 q^{66} - 11112 q^{67} - 10800 q^{69} - 2208 q^{72} - 8988 q^{73} + 792 q^{78} - 10704 q^{79} + 7242 q^{81} - 7848 q^{82} - 6900 q^{87} - 240 q^{90} + 8952 q^{91} - 7740 q^{97} - 1668 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)