# Properties

 Label 3150.2.dk Level 3150 Weight 2 Character orbit dk Rep. character $$\chi_{3150}(209,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1920 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.dk (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1575$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$1440$$

## Dimensions

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

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

## Trace form

 $$1920q + 240q^{4} + O(q^{10})$$ $$1920q + 240q^{4} + 20q^{15} + 240q^{16} + 24q^{21} + 28q^{30} + 92q^{39} - 36q^{50} - 24q^{51} + 28q^{60} + 50q^{63} - 480q^{64} + 72q^{65} + 24q^{70} + 240q^{77} - 24q^{79} + 88q^{81} + 18q^{84} + 60q^{92} + 12q^{95} + 32q^{99} + O(q^{100})$$

## 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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database