# Properties

 Label 1050.3.e Level $1050$ Weight $3$ Character orbit 1050.e Rep. character $\chi_{1050}(701,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $5$ Sturm bound $720$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$720$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 504 76 428
Cusp forms 456 76 380
Eisenstein series 48 0 48

## Trace form

 $$76 q + 8 q^{3} - 152 q^{4} - 8 q^{6} - 12 q^{9} + O(q^{10})$$ $$76 q + 8 q^{3} - 152 q^{4} - 8 q^{6} - 12 q^{9} - 16 q^{12} - 40 q^{13} + 304 q^{16} + 32 q^{18} + 16 q^{19} + 28 q^{21} + 56 q^{22} + 16 q^{24} - 64 q^{27} + 144 q^{31} + 48 q^{33} - 208 q^{34} + 24 q^{36} - 160 q^{37} - 56 q^{39} + 256 q^{43} + 40 q^{46} + 32 q^{48} + 532 q^{49} + 104 q^{51} + 80 q^{52} + 40 q^{54} + 264 q^{57} + 64 q^{58} - 56 q^{61} - 112 q^{63} - 608 q^{64} + 144 q^{66} - 480 q^{67} - 192 q^{69} - 64 q^{72} - 168 q^{73} - 32 q^{76} - 128 q^{78} + 208 q^{79} - 300 q^{81} + 368 q^{82} - 56 q^{84} + 280 q^{87} - 112 q^{88} - 224 q^{91} + 176 q^{93} - 208 q^{94} - 32 q^{96} + 552 q^{97} + 1352 q^{99} + O(q^{100})$$

## 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.e.a $4$ $28.610$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2+\cdots)q^{6}+\cdots$$
1050.3.e.b $16$ $28.610$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+\beta _{2}q^{3}-2q^{4}-\beta _{9}q^{6}+\beta _{6}q^{7}+\cdots$$
1050.3.e.c $16$ $28.610$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{2}q^{3}-2q^{4}-\beta _{9}q^{6}-\beta _{6}q^{7}+\cdots$$
1050.3.e.d $16$ $28.610$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{6}q^{3}-2q^{4}+(1+\beta _{7})q^{6}+\cdots$$
1050.3.e.e $24$ $28.610$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$