# Properties

 Label 1575.2.ch Level 1575 Weight 2 Character orbit ch Rep. character $$\chi_{1575}(82,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 232 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.ch (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$35$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$480$$

## Dimensions

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

Total New Old
Modular forms 1056 248 808
Cusp forms 864 232 632
Eisenstein series 192 16 176

## Trace form

 $$232q - 2q^{2} + 2q^{7} - 28q^{8} + O(q^{10})$$ $$232q - 2q^{2} + 2q^{7} - 28q^{8} + 4q^{11} + 84q^{16} + 12q^{17} + 8q^{22} + 2q^{23} + 36q^{26} + 70q^{28} + 12q^{31} + 6q^{32} + 16q^{37} + 28q^{43} - 8q^{46} - 36q^{47} - 24q^{52} - 4q^{53} + 8q^{56} - 66q^{58} + 48q^{61} - 18q^{67} + 120q^{68} + 64q^{71} - 48q^{73} + 40q^{77} - 18q^{82} + 112q^{86} - 16q^{88} - 52q^{91} - 92q^{92} - 54q^{98} + O(q^{100})$$

## 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