# Properties

 Label 950.2.j Level $950$ Weight $2$ Character orbit 950.j Rep. character $\chi_{950}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $60$ Newform subspaces $9$ Sturm bound $300$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$300$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(950, [\chi])$$.

Total New Old
Modular forms 324 60 264
Cusp forms 276 60 216
Eisenstein series 48 0 48

## Trace form

 $$60q + 30q^{4} + 30q^{9} + O(q^{10})$$ $$60q + 30q^{4} + 30q^{9} + 16q^{11} + 12q^{14} - 30q^{16} - 4q^{19} - 28q^{21} - 16q^{26} + 4q^{29} - 8q^{31} + 8q^{34} - 30q^{36} + 88q^{39} + 12q^{41} + 8q^{44} + 56q^{46} - 100q^{49} + 2q^{51} + 24q^{56} + 30q^{59} + 16q^{61} - 60q^{64} + 6q^{66} - 80q^{69} + 52q^{71} - 20q^{74} - 20q^{76} - 4q^{79} - 46q^{81} - 56q^{84} - 40q^{86} - 16q^{89} - 52q^{91} + 80q^{94} + 34q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(950, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
950.2.j.a $$4$$ $$7.586$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots$$
950.2.j.b $$4$$ $$7.586$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots$$
950.2.j.c $$4$$ $$7.586$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+4\zeta_{12}^{3}q^{7}+\cdots$$
950.2.j.d $$4$$ $$7.586$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$$
950.2.j.e $$4$$ $$7.586$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots$$
950.2.j.f $$8$$ $$7.586$$ 8.0.1731891456.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$$
950.2.j.g $$8$$ $$7.586$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1+\beta _{3})q^{4}+\beta _{7}q^{6}+\cdots$$
950.2.j.h $$8$$ $$7.586$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(1-\beta _{5})q^{4}+\cdots$$
950.2.j.i $$16$$ $$7.586$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{14}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(950, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$