# Properties

 Label 1575.2.p Level 1575 Weight 2 Character orbit p Rep. character $$\chi_{1575}(118,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 116 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$35$$ Character field: $$\Q(i)$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 528 124 404
Cusp forms 432 116 316
Eisenstein series 96 8 88

## Trace form

 $$116q - 4q^{2} + 4q^{7} + 16q^{8} + O(q^{10})$$ $$116q - 4q^{2} + 4q^{7} + 16q^{8} - 16q^{11} - 144q^{16} + 28q^{22} - 32q^{23} + 8q^{28} + 48q^{32} + 8q^{37} - 4q^{43} - 52q^{46} + 28q^{53} - 20q^{56} - 12q^{58} - 60q^{67} + 104q^{71} - 28q^{77} + 140q^{86} - 56q^{88} - 56q^{91} - 40q^{92} - 108q^{98} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database