# Properties

 Label 525.4.j Level $525$ Weight $4$ Character orbit 525.j Rep. character $\chi_{525}(218,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $216$ Sturm bound $320$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 525.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Sturm bound: $$320$$

## Dimensions

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

Total New Old
Modular forms 504 216 288
Cusp forms 456 216 240
Eisenstein series 48 0 48

## Trace form

 $$216q - 8q^{3} + O(q^{10})$$ $$216q - 8q^{3} + 128q^{12} + 144q^{13} - 2544q^{16} - 460q^{18} - 224q^{21} - 576q^{22} + 592q^{27} + 1920q^{31} + 56q^{33} - 1856q^{36} - 2088q^{37} + 140q^{42} - 240q^{43} - 1056q^{46} - 3208q^{48} + 1720q^{51} - 240q^{52} + 1112q^{57} - 840q^{58} + 3648q^{61} + 1064q^{63} + 2576q^{66} + 2832q^{67} + 296q^{72} - 1776q^{73} - 14592q^{76} + 4500q^{78} + 4288q^{81} - 1680q^{82} + 392q^{87} + 5352q^{88} - 2016q^{91} + 5488q^{93} + 576q^{96} + 7872q^{97} + O(q^{100})$$

## 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

$$S_{4}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database