# Properties

 Label 3150.2.dq Level 3150 Weight 2 Character orbit dq Rep. character $$\chi_{3150}(169,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1440 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.dq (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ 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 1440 4384
Cusp forms 5696 1440 4256
Eisenstein series 128 0 128

## Trace form

 $$1440q - 180q^{4} + 16q^{5} - 8q^{9} + O(q^{10})$$ $$1440q - 180q^{4} + 16q^{5} - 8q^{9} + 8q^{11} - 20q^{12} - 8q^{14} + 20q^{15} + 180q^{16} + 4q^{20} - 48q^{25} - 24q^{29} + 16q^{30} - 24q^{31} - 16q^{36} + 12q^{39} + 16q^{44} + 144q^{45} + 100q^{47} + 40q^{48} + 720q^{49} - 4q^{50} + 40q^{51} + 48q^{54} - 24q^{55} + 8q^{56} - 12q^{59} + 16q^{60} + 20q^{63} + 360q^{64} + 152q^{65} + 60q^{67} - 68q^{69} - 80q^{71} + 160q^{74} + 40q^{78} + 8q^{80} - 16q^{81} - 24q^{85} + 40q^{86} + 300q^{87} - 160q^{89} - 60q^{90} + 60q^{92} + 12q^{95} + 88q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database