# Properties

 Label 1050.3.c Level $1050$ Weight $3$ Character orbit 1050.c Rep. character $\chi_{1050}(449,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $3$ Sturm bound $720$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$720$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1050, [\chi])$$.

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

## Trace form

 $$72 q + 144 q^{4} - 48 q^{9} + O(q^{10})$$ $$72 q + 144 q^{4} - 48 q^{9} + 288 q^{16} + 80 q^{19} + 56 q^{21} - 208 q^{31} - 96 q^{34} - 96 q^{36} + 104 q^{39} + 208 q^{46} - 504 q^{49} + 488 q^{51} + 288 q^{54} + 576 q^{64} + 32 q^{66} + 344 q^{69} + 160 q^{76} - 16 q^{79} - 336 q^{81} + 112 q^{84} - 336 q^{91} + 256 q^{94} - 648 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1050, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.3.c.a $8$ $28.610$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(-2+\cdots)q^{6}+\cdots$$
1050.3.c.b $32$ $28.610$ None $$0$$ $$0$$ $$0$$ $$0$$
1050.3.c.c $32$ $28.610$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1050, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$