# Properties

 Label 525.4.w Level $525$ Weight $4$ Character orbit 525.w Rep. character $\chi_{525}(104,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $944$ Sturm bound $320$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 525.w (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$525$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$320$$

## Dimensions

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

Total New Old
Modular forms 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

## Trace form

 $$944q - 940q^{4} - 6q^{9} + O(q^{10})$$ $$944q - 940q^{4} - 6q^{9} + 198q^{15} - 3532q^{16} - 108q^{21} + 340q^{22} - 232q^{25} + 270q^{28} + 326q^{30} - 128q^{36} - 20q^{37} + 1114q^{39} - 1085q^{42} + 1540q^{46} + 980q^{49} - 1300q^{51} + 3400q^{58} + 2656q^{60} + 3160q^{63} - 11972q^{64} - 20q^{67} - 3020q^{70} + 630q^{72} - 280q^{78} - 1188q^{79} - 2482q^{81} - 2068q^{84} - 6948q^{85} + 8080q^{88} - 1020q^{91} - 4116q^{99} + O(q^{100})$$

## 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