# Properties

 Label 3150.2.ch Level 3150 Weight 2 Character orbit ch Rep. character $$\chi_{3150}(643,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 576 Sturm bound 1440

# Related objects

## Defining parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.ch (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$1440$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3150, [\chi])$$.

Total New Old
Modular forms 2976 576 2400
Cusp forms 2784 576 2208
Eisenstein series 192 0 192

## Trace form

 $$576q + O(q^{10})$$ $$576q - 16q^{11} + 288q^{16} + 8q^{18} - 8q^{23} - 16q^{36} + 44q^{42} - 96q^{46} + 160q^{53} + 8q^{56} - 88q^{57} - 24q^{58} + 48q^{63} - 32q^{71} - 16q^{72} + 16q^{77} + 16q^{78} + 16q^{81} + 32q^{86} - 8q^{92} + 120q^{93} + 48q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3150, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(3150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database