# Properties

 Label 350.2.j Level $350$ Weight $2$ Character orbit 350.j Rep. character $\chi_{350}(149,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $6$ Sturm bound $120$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$350 = 2 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 350.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$120$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(350, [\chi])$$.

Total New Old
Modular forms 144 24 120
Cusp forms 96 24 72
Eisenstein series 48 0 48

## Trace form

 $$24q + 12q^{4} + 16q^{6} + 8q^{9} + O(q^{10})$$ $$24q + 12q^{4} + 16q^{6} + 8q^{9} + 8q^{11} + 4q^{14} - 12q^{16} + 4q^{19} - 20q^{21} + 8q^{24} - 16q^{26} - 24q^{29} - 12q^{31} - 16q^{34} + 16q^{36} - 32q^{39} - 8q^{41} - 8q^{44} - 24q^{46} + 48q^{49} + 12q^{51} + 20q^{54} - 4q^{56} + 4q^{59} + 16q^{61} - 24q^{64} - 8q^{71} + 12q^{74} + 8q^{76} - 28q^{79} + 28q^{81} - 4q^{84} + 16q^{86} + 16q^{89} - 4q^{91} - 4q^{94} - 8q^{96} - 48q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(350, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
350.2.j.a $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$$
350.2.j.b $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
350.2.j.c $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots$$
350.2.j.d $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
350.2.j.e $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
350.2.j.f $$4$$ $$2.795$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(350, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(350, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$