Properties

Label 525.4.i
Level $525$
Weight $4$
Character orbit 525.i
Rep. character $\chi_{525}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $152$
Sturm bound $320$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 504 152 352
Cusp forms 456 152 304
Eisenstein series 48 0 48

Trace form

\( 152q + 2q^{2} + 6q^{3} - 314q^{4} + 24q^{6} - 24q^{7} - 48q^{8} - 684q^{9} + O(q^{10}) \) \( 152q + 2q^{2} + 6q^{3} - 314q^{4} + 24q^{6} - 24q^{7} - 48q^{8} - 684q^{9} - 20q^{11} + 72q^{12} - 4q^{13} + 322q^{14} - 1210q^{16} + 124q^{17} + 18q^{18} - 258q^{19} + 132q^{21} + 700q^{22} - 196q^{23} - 234q^{24} - 34q^{26} - 108q^{27} + 934q^{28} - 872q^{29} - 568q^{31} - 56q^{32} + 114q^{33} + 1752q^{34} + 5652q^{36} + 606q^{37} - 294q^{38} + 462q^{39} - 1208q^{41} - 408q^{42} - 396q^{43} - 20q^{44} + 1316q^{46} - 608q^{47} - 816q^{48} + 1080q^{49} + 228q^{51} + 1168q^{52} - 1396q^{53} - 108q^{54} - 4572q^{56} - 276q^{57} - 2554q^{58} + 1288q^{59} - 1908q^{61} + 2724q^{62} + 162q^{63} + 10612q^{64} + 156q^{66} - 770q^{67} + 5016q^{68} + 600q^{69} + 4688q^{71} + 216q^{72} + 2322q^{73} - 1910q^{74} + 7152q^{76} - 3108q^{77} - 1980q^{78} - 1772q^{79} - 6156q^{81} - 1288q^{82} + 296q^{83} - 3816q^{84} - 1646q^{86} + 1038q^{87} - 1438q^{88} + 3872q^{89} - 4594q^{91} + 7424q^{92} - 894q^{93} + 76q^{94} - 3354q^{96} + 396q^{97} + 9052q^{98} + 360q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database