# Properties

 Label 1575.2.bp Level 1575 Weight 2 Character orbit bp Rep. character $$\chi_{1575}(949,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 280 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.bp (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

## Trace form

 $$280q + 134q^{4} - 20q^{6} + 2q^{9} + O(q^{10})$$ $$280q + 134q^{4} - 20q^{6} + 2q^{9} - 12q^{11} - 10q^{14} - 122q^{16} + 4q^{19} + 10q^{21} - 28q^{24} + 24q^{26} + 24q^{29} + 2q^{31} - 40q^{36} + 24q^{41} - 24q^{46} + 26q^{49} - 10q^{51} - 26q^{54} + 12q^{56} - 50q^{59} - 10q^{61} - 184q^{64} + 102q^{66} + 60q^{69} - 60q^{71} + 100q^{74} - 4q^{76} - 2q^{79} + 78q^{81} + 38q^{84} + 108q^{86} - 26q^{89} + 20q^{91} - 42q^{94} - 58q^{96} + 50q^{99} + O(q^{100})$$

## 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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database