# Properties

 Label 1575.2.dg Level 1575 Weight 2 Character orbit dg Rep. character $$\chi_{1575}(206,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 640 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.dg (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$525$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

## Trace form

 $$640q - 80q^{4} + 8q^{7} + O(q^{10})$$ $$640q - 80q^{4} + 8q^{7} + 12q^{10} + 80q^{16} + 32q^{22} + 4q^{25} + 100q^{28} + 36q^{31} + 16q^{37} - 24q^{40} + 16q^{43} - 64q^{46} + 16q^{49} + 96q^{58} + 256q^{64} + 32q^{67} + 120q^{70} - 168q^{73} + 8q^{79} - 264q^{82} - 8q^{85} - 84q^{88} + 68q^{91} - 96q^{94} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database