Properties

Label 525.4.bp
Level $525$
Weight $4$
Character orbit 525.bp
Rep. character $\chi_{525}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
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.bp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888q - 15q^{3} + 922q^{4} - 3q^{9} + O(q^{10}) \) \( 1888q - 15q^{3} + 922q^{4} - 3q^{9} - 60q^{10} - 15q^{12} + 306q^{15} + 3610q^{16} - 18q^{19} + 99q^{21} + 680q^{22} - 246q^{24} - 170q^{25} - 300q^{28} + 313q^{30} + 1224q^{31} + 2385q^{33} - 880q^{36} - 10q^{37} - 541q^{39} - 60q^{40} - 2170q^{42} + 2088q^{45} - 298q^{46} - 1028q^{49} - 488q^{51} - 30q^{52} - 57q^{54} - 3430q^{58} - 1189q^{60} - 18q^{61} - 3175q^{63} - 25192q^{64} + 2757q^{66} - 10q^{67} + 4580q^{70} - 645q^{72} + 6810q^{73} - 8130q^{75} + 250q^{78} - 594q^{79} - 215q^{81} + 3355q^{84} + 7764q^{85} - 15q^{87} + 7010q^{88} - 5172q^{91} + 270q^{94} + 1719q^{96} + 516q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database