# Properties

 Label 3150.2.bu Level 3150 Weight 2 Character orbit bu Rep. character $$\chi_{3150}(379,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 304 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.bu (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$25$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$1440$$

## Dimensions

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

Total New Old
Modular forms 2944 304 2640
Cusp forms 2816 304 2512
Eisenstein series 128 0 128

## Trace form

 $$304q + 76q^{4} - 16q^{5} + O(q^{10})$$ $$304q + 76q^{4} - 16q^{5} + 4q^{11} - 4q^{14} - 76q^{16} + 24q^{19} - 4q^{20} + 20q^{22} - 20q^{23} - 88q^{25} + 8q^{26} - 32q^{29} - 24q^{31} + 12q^{34} - 4q^{35} + 8q^{41} - 4q^{44} - 20q^{46} - 140q^{47} - 304q^{49} + 12q^{50} + 20q^{53} + 12q^{55} + 4q^{56} + 36q^{59} - 40q^{61} + 76q^{64} + 80q^{65} + 140q^{67} - 4q^{70} - 32q^{71} + 80q^{73} + 72q^{74} + 16q^{76} + 40q^{77} + 56q^{79} + 4q^{80} + 60q^{83} + 96q^{85} + 20q^{86} + 76q^{89} - 4q^{91} + 4q^{95} + 60q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database