# Properties

 Label 1575.2.ba Level 1575 Weight 2 Character orbit ba Rep. character $$\chi_{1575}(524,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 280 Sturm bound 480

# Learn more about

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.ba (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

 $$280q - 132q^{4} - 8q^{9} + O(q^{10})$$ $$280q - 132q^{4} - 8q^{9} - 24q^{11} + 18q^{14} - 124q^{16} - 6q^{21} + 84q^{29} + 84q^{36} - 48q^{39} + 16q^{46} + 14q^{49} + 12q^{51} - 96q^{56} + 224q^{64} + 36q^{74} + 40q^{79} - 40q^{81} + 54q^{84} - 288q^{86} - 36q^{91} + 116q^{99} + O(q^{100})$$

## 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