# Properties

 Label 3150.2.bb Level 3150 Weight 2 Character orbit bb Rep. character $$\chi_{3150}(499,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 288 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.bb (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$1440$$

## Dimensions

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

Total New Old
Modular forms 1488 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

## Trace form

 $$288q - 288q^{4} + 8q^{6} - 16q^{9} + O(q^{10})$$ $$288q - 288q^{4} + 8q^{6} - 16q^{9} - 8q^{11} + 4q^{14} + 288q^{16} - 4q^{21} - 8q^{24} - 24q^{26} - 20q^{29} + 16q^{36} - 52q^{39} - 28q^{41} + 8q^{44} + 12q^{46} + 12q^{49} - 32q^{51} + 16q^{54} - 4q^{56} - 48q^{59} - 24q^{61} - 288q^{64} - 32q^{66} - 44q^{69} + 40q^{71} - 24q^{79} + 40q^{81} + 4q^{84} - 8q^{86} + 64q^{89} - 48q^{94} + 8q^{96} - 24q^{99} + O(q^{100})$$

## 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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database