# Properties

 Label 3150.3.c Level $3150$ Weight $3$ Character orbit 3150.c Rep. character $\chi_{3150}(449,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $6$ Sturm bound $2160$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 3150.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$2160$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(3150, [\chi])$$.

Total New Old
Modular forms 1488 72 1416
Cusp forms 1392 72 1320
Eisenstein series 96 0 96

## Trace form

 $$72 q + 144 q^{4} + O(q^{10})$$ $$72 q + 144 q^{4} + 288 q^{16} - 160 q^{19} - 64 q^{31} - 48 q^{34} - 416 q^{46} - 504 q^{49} + 240 q^{61} + 576 q^{64} - 320 q^{76} + 128 q^{79} - 512 q^{94} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(3150, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3150.3.c.a $8$ $85.831$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{6}q^{8}+\cdots$$
3150.3.c.b $8$ $85.831$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots$$
3150.3.c.c $8$ $85.831$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+2q^{4}-\beta _{1}q^{7}+2\beta _{6}q^{8}+\cdots$$
3150.3.c.d $16$ $85.831$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+2q^{4}-\beta _{2}q^{7}-2\beta _{5}q^{8}+\cdots$$
3150.3.c.e $16$ $85.831$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+2q^{4}-\beta _{10}q^{7}+2\beta _{2}q^{8}+\cdots$$
3150.3.c.f $16$ $85.831$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+2q^{4}+\beta _{2}q^{7}-2\beta _{6}q^{8}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(3150, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$