# Properties

 Label 3150.2.db Level 3150 Weight 2 Character orbit db Rep. character $$\chi_{3150}(89,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 640 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.db (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$525$$ 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 5888 640 5248
Cusp forms 5632 640 4992
Eisenstein series 256 0 256

## Trace form

 $$640q + 80q^{4} + O(q^{10})$$ $$640q + 80q^{4} - 12q^{10} + 80q^{16} - 80q^{22} + 12q^{25} - 20q^{28} + 36q^{31} + 12q^{40} - 24q^{46} + 8q^{49} - 160q^{64} - 12q^{70} - 240q^{73} - 8q^{79} - 48q^{85} + 20q^{88} + 104q^{91} + 96q^{94} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database