# 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

## 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