# Properties

 Label 1575.2.q Level 1575 Weight 2 Character orbit q Rep. character $$\chi_{1575}(316,\cdot)$$ Character field $$\Q(\zeta_{5})$$ Dimension 304 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.q (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$25$$ Character field: $$\Q(\zeta_{5})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 992 304 688
Cusp forms 928 304 624
Eisenstein series 64 0 64

## Trace form

 $$304q - 2q^{2} - 78q^{4} - 12q^{5} - 6q^{8} + O(q^{10})$$ $$304q - 2q^{2} - 78q^{4} - 12q^{5} - 6q^{8} + 6q^{10} + 8q^{11} + 4q^{14} - 106q^{16} - 16q^{17} - 12q^{19} + 52q^{20} + 34q^{22} + 18q^{23} + 2q^{25} - 32q^{26} + 2q^{29} - 12q^{31} + 56q^{32} + 18q^{34} - 2q^{35} + 8q^{37} - 46q^{38} - 36q^{40} - 24q^{41} + 36q^{43} + 62q^{44} - 20q^{46} + 10q^{47} + 304q^{49} + 76q^{50} + 28q^{52} + 46q^{53} + 94q^{55} + 12q^{56} + 2q^{58} - 18q^{59} - 40q^{61} + 74q^{62} - 114q^{64} + 28q^{65} + 18q^{67} - 12q^{68} + 16q^{70} + 64q^{71} - 68q^{73} - 64q^{74} + 12q^{76} + 12q^{77} - 48q^{79} - 138q^{80} - 148q^{82} + 6q^{83} - 14q^{85} + 100q^{86} - 132q^{88} + 68q^{89} - 8q^{91} + 40q^{92} + 40q^{94} + 122q^{95} - 18q^{97} - 2q^{98} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database