# Properties

 Label 950.2.q Level $950$ Weight $2$ Character orbit 950.q Rep. character $\chi_{950}(107,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $120$ Newform subspaces $7$ Sturm bound $300$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.q (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$7$$ Sturm bound: $$300$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 648 120 528
Cusp forms 552 120 432
Eisenstein series 96 0 96

## Trace form

 $$120q - 8q^{7} + O(q^{10})$$ $$120q - 8q^{7} + 16q^{11} + 60q^{16} + 16q^{17} - 24q^{21} + 24q^{22} - 4q^{23} + 32q^{26} + 4q^{28} + 12q^{33} - 60q^{36} - 4q^{38} - 24q^{41} - 32q^{42} + 4q^{43} + 36q^{47} - 132q^{51} + 36q^{53} + 36q^{57} - 8q^{61} - 8q^{62} + 8q^{63} + 44q^{66} - 24q^{67} - 32q^{68} - 24q^{73} + 24q^{76} + 64q^{77} + 24q^{78} + 60q^{81} - 8q^{82} - 64q^{83} - 48q^{86} - 152q^{87} - 264q^{91} + 4q^{92} - 28q^{93} + 12q^{97} - 120q^{98} + O(q^{100})$$

## 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.q.a $$8$$ $$7.586$$ $$\Q(\zeta_{24})$$ None $$0$$ $$-12$$ $$0$$ $$16$$ $$q-\zeta_{24}q^{2}+(-2+\zeta_{24}^{2}+\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$
950.2.q.b $$8$$ $$7.586$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots$$
950.2.q.c $$8$$ $$7.586$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(1+\cdots)q^{6}+\cdots$$
950.2.q.d $$8$$ $$7.586$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}+2\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$$
950.2.q.e $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.q.f $$32$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.q.g $$32$$ $$7.586$$ None $$0$$ $$12$$ $$0$$ $$-24$$

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

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