# Properties

 Label 1575.2.k Level 1575 Weight 2 Character orbit k Rep. character $$\chi_{1575}(1201,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 292 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.k (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$63$$ Character field: $$\Q(\zeta_{3})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

## Trace form

 $$292q - q^{2} + q^{3} - 141q^{4} - 14q^{6} + 2q^{7} + 12q^{8} + q^{9} + O(q^{10})$$ $$292q - q^{2} + q^{3} - 141q^{4} - 14q^{6} + 2q^{7} + 12q^{8} + q^{9} - 10q^{11} + q^{12} + q^{13} + 25q^{14} - 127q^{16} + 7q^{17} + 11q^{18} + 4q^{19} + 14q^{21} + 6q^{22} - 12q^{23} + 12q^{24} - 16q^{26} + q^{27} + 14q^{28} - 8q^{29} - q^{31} - 13q^{32} + 20q^{33} + 8q^{34} - 32q^{36} + q^{37} - 50q^{38} + 28q^{39} - 30q^{41} - 5q^{42} - 2q^{43} + 35q^{44} - 8q^{46} + 25q^{47} + 69q^{48} - 10q^{49} + 14q^{51} - 14q^{52} + 12q^{53} - 32q^{54} - 24q^{56} - 25q^{57} - 18q^{58} - 20q^{59} - 10q^{61} + 36q^{62} - 6q^{63} + 212q^{64} + 53q^{66} - 8q^{67} - 56q^{68} - 10q^{69} - 66q^{71} - 11q^{72} + 16q^{73} - 14q^{74} + 18q^{76} + 16q^{77} - 5q^{78} + 10q^{79} - 35q^{81} + 50q^{83} - 45q^{84} + 10q^{86} - 7q^{87} - 6q^{88} - 41q^{89} - 15q^{91} + 70q^{92} + 48q^{93} + 35q^{94} - 52q^{96} + q^{97} - 51q^{98} + 20q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database