# Properties

 Label 3150.2.dv Level 3150 Weight 2 Character orbit dv Rep. character $$\chi_{3150}(109,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 800 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.dv (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ 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 800 5088
Cusp forms 5632 800 4832
Eisenstein series 256 0 256

## Trace form

 $$800q - 100q^{4} - 2q^{5} + O(q^{10})$$ $$800q - 100q^{4} - 2q^{5} + 2q^{10} - 6q^{11} + 100q^{16} - 20q^{17} + 4q^{19} - 4q^{20} - 40q^{22} - 30q^{23} - 12q^{25} - 48q^{26} + 10q^{28} + 24q^{29} + 6q^{31} - 16q^{34} - 4q^{35} - 2q^{40} + 4q^{41} - 4q^{44} - 12q^{46} - 16q^{50} - 20q^{53} + 16q^{55} - 8q^{61} + 120q^{62} + 200q^{64} - 34q^{65} - 10q^{70} - 4q^{71} + 40q^{73} + 16q^{74} - 32q^{76} + 80q^{77} - 2q^{80} + 120q^{83} - 68q^{85} + 12q^{86} + 10q^{88} - 54q^{89} + 4q^{91} + 40q^{92} + 32q^{94} + 44q^{95} + 20q^{97} + 40q^{98} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database