# Properties

 Label 1575.2.dv Level 1575 Weight 2 Character orbit dv Rep. character $$\chi_{1575}(59,\cdot)$$ 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.dv (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

 $$1888q - 15q^{2} - 15q^{3} + 235q^{4} - 24q^{5} - 12q^{6} - 3q^{9} + O(q^{10})$$ $$1888q - 15q^{2} - 15q^{3} + 235q^{4} - 24q^{5} - 12q^{6} - 3q^{9} - 24q^{10} - 15q^{12} - 9q^{14} - 54q^{15} + 223q^{16} - 18q^{19} - 6q^{20} - 18q^{21} - 10q^{22} - 6q^{24} - 8q^{25} - 12q^{26} - 18q^{29} + 13q^{30} - 9q^{31} + 60q^{33} - 12q^{34} + 75q^{35} - 40q^{36} - 10q^{37} - 30q^{38} - 37q^{39} + 20q^{42} - 60q^{44} - 3q^{45} + 2q^{46} - 15q^{47} - 30q^{48} - 8q^{49} - 60q^{50} - 8q^{51} - 9q^{54} - 72q^{56} - 10q^{58} - 9q^{59} - 109q^{60} - 9q^{61} + 180q^{62} + 5q^{63} - 436q^{64} - 69q^{65} - 93q^{66} + 5q^{67} - 45q^{69} - 40q^{70} - 45q^{72} - 30q^{73} - 27q^{75} - 48q^{76} - 15q^{77} + 10q^{78} - 9q^{79} + 216q^{80} + q^{81} + 19q^{84} - 3q^{85} - 15q^{87} - 10q^{88} - 45q^{89} - 162q^{90} + 30q^{91} - 210q^{92} - 9q^{94} + 78q^{95} + 39q^{96} - 30q^{98} - 66q^{99} + O(q^{100})$$

## 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