# Properties

 Label 1575.2.dq Level 1575 Weight 2 Character orbit dq Rep. character $$\chi_{1575}(104,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1888 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.dq (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1575$$ 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 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

## Trace form

 $$1888q - 30q^{2} + 226q^{4} - 12q^{9} + O(q^{10})$$ $$1888q - 30q^{2} + 226q^{4} - 12q^{9} - 18q^{11} - 9q^{14} - 36q^{15} + 226q^{16} - 9q^{21} - 10q^{22} - 30q^{23} - 8q^{25} - 60q^{28} - 18q^{29} - 56q^{30} - 46q^{36} - 40q^{37} - 76q^{39} + 20q^{42} - 40q^{46} - 8q^{49} + 12q^{50} - 32q^{51} - 84q^{56} - 10q^{58} - 16q^{60} - 70q^{63} - 448q^{64} - 30q^{65} - 10q^{67} - 64q^{70} - 60q^{72} - 72q^{74} - 135q^{77} - 80q^{78} + 18q^{79} - 116q^{81} + 43q^{84} - 18q^{85} - 78q^{86} - 10q^{88} + 30q^{91} - 210q^{92} - 6q^{95} - 12q^{99} + O(q^{100})$$

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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database