# Properties

 Label 3150.2.co Level 3150 Weight 2 Character orbit co Rep. character $$\chi_{3150}(157,\cdot)$$ 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.co (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

 $$576q + O(q^{10})$$ $$576q + 32q^{11} + 288q^{16} - 36q^{17} - 16q^{18} - 24q^{21} + 16q^{23} + 36q^{27} + 60q^{33} + 32q^{36} - 24q^{41} - 4q^{42} - 24q^{46} - 48q^{51} + 40q^{53} - 16q^{56} + 32q^{57} - 24q^{58} - 72q^{61} + 108q^{63} - 32q^{71} + 8q^{72} - 80q^{77} + 16q^{78} - 8q^{81} + 168q^{83} + 32q^{86} - 8q^{92} + 60q^{93} + 24q^{96} + 48q^{98} + O(q^{100})$$

## 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