# Properties

 Label 1575.2.s Level 1575 Weight 2 Character orbit s Rep. character $$\chi_{1575}(499,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 280 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1575, [\chi])$$.

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

## Trace form

 $$280q - 268q^{4} - 20q^{6} + 14q^{9} + O(q^{10})$$ $$280q - 268q^{4} - 20q^{6} + 14q^{9} + 6q^{11} + 14q^{14} + 244q^{16} + 4q^{19} - 8q^{21} + 56q^{24} + 24q^{26} + 24q^{29} - 4q^{31} - 40q^{36} + 54q^{39} + 24q^{41} - 24q^{46} - 10q^{49} + 62q^{51} - 38q^{54} - 96q^{56} + 100q^{59} + 20q^{61} - 184q^{64} - 24q^{66} + 60q^{69} - 60q^{71} - 50q^{74} - 4q^{76} + 4q^{79} - 54q^{81} - 4q^{84} - 54q^{86} - 26q^{89} + 20q^{91} + 84q^{94} - 190q^{96} + 50q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database