# Properties

 Label 1050.3.q Level $1050$ Weight $3$ Character orbit 1050.q Rep. character $\chi_{1050}(199,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $5$ Sturm bound $720$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$720$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

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

Total New Old
Modular forms 1008 96 912
Cusp forms 912 96 816
Eisenstein series 96 0 96

## Trace form

 $$96q + 96q^{4} - 144q^{9} + O(q^{10})$$ $$96q + 96q^{4} - 144q^{9} - 56q^{11} + 32q^{14} - 192q^{16} - 156q^{19} - 12q^{21} - 192q^{26} - 192q^{29} - 24q^{31} - 576q^{36} - 36q^{39} + 112q^{44} + 16q^{46} + 244q^{49} + 48q^{51} + 128q^{56} - 1008q^{59} + 204q^{61} - 768q^{64} - 32q^{71} + 512q^{74} - 136q^{79} - 432q^{81} - 48q^{84} - 368q^{86} + 96q^{89} - 1612q^{91} - 576q^{94} + 336q^{99} + O(q^{100})$$

## 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.q.a $$8$$ $$28.610$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{5}q^{2}+(\zeta_{24}-2\zeta_{24}^{3})q^{3}+(2+\cdots)q^{4}+\cdots$$
1050.3.q.b $$16$$ $$28.610$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(2+2\beta _{3}+\cdots)q^{4}+\cdots$$
1050.3.q.c $$16$$ $$28.610$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{13}q^{2}+(\beta _{1}+2\beta _{8})q^{3}-2\beta _{6}q^{4}+\cdots$$
1050.3.q.d $$24$$ $$28.610$$ None $$0$$ $$0$$ $$0$$ $$0$$
1050.3.q.e $$32$$ $$28.610$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$