# Properties

 Label 3150.2.de Level 3150 Weight 2 Character orbit de Rep. character $$\chi_{3150}(41,\cdot)$$ 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.de (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

 $$1920q - 240q^{4} + O(q^{10})$$ $$1920q - 240q^{4} - 44q^{15} + 240q^{16} + 8q^{18} - 24q^{21} + 24q^{23} + 20q^{30} + 92q^{39} + 20q^{42} - 60q^{50} + 24q^{51} - 184q^{57} + 24q^{58} - 20q^{60} - 14q^{63} + 480q^{64} - 96q^{65} - 24q^{70} + 16q^{72} + 96q^{77} - 16q^{78} - 24q^{79} - 88q^{81} + 18q^{84} - 36q^{92} + 184q^{93} - 12q^{95} + 32q^{99} + O(q^{100})$$

## 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