# Properties

 Label 1575.2.cf Level 1575 Weight 2 Character orbit cf Rep. character $$\chi_{1575}(32,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 560 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.cf (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

## Trace form

 $$560q + 6q^{2} + 2q^{3} + 2q^{7} + O(q^{10})$$ $$560q + 6q^{2} + 2q^{3} + 2q^{7} + 22q^{12} + 4q^{13} + 260q^{16} + 18q^{17} + 10q^{18} - 64q^{21} - 4q^{22} + 32q^{27} + 4q^{28} + 4q^{31} + 90q^{32} - 32q^{33} - 16q^{36} + 4q^{37} - 14q^{42} + 4q^{43} - 32q^{46} + 6q^{47} - 38q^{48} - 52q^{51} + 52q^{52} + 156q^{56} - 32q^{57} + 12q^{58} + 28q^{61} - 14q^{63} + 244q^{66} - 2q^{67} + 46q^{72} + 4q^{73} - 24q^{76} - 42q^{77} - 54q^{78} - 52q^{81} + 8q^{82} + 12q^{83} + 28q^{87} - 12q^{88} - 16q^{91} - 72q^{92} - 4q^{93} + 36q^{96} + 4q^{97} - 12q^{98} + O(q^{100})$$

## 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