# Properties

 Label 950.2.u Level $950$ Weight $2$ Character orbit 950.u Rep. character $\chi_{950}(99,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $180$ Newform subspaces $8$ Sturm bound $300$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.u (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$8$$ Sturm bound: $$300$$ Trace bound: $$9$$ 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 972 180 792
Cusp forms 828 180 648
Eisenstein series 144 0 144

## Trace form

 $$180q + O(q^{10})$$ $$180q - 12q^{11} + 24q^{14} - 24q^{19} + 24q^{21} - 12q^{26} + 24q^{29} - 96q^{39} + 12q^{41} - 12q^{44} + 150q^{49} + 150q^{51} + 36q^{54} + 48q^{56} - 6q^{59} + 84q^{61} + 90q^{64} + 126q^{66} + 48q^{69} - 36q^{74} + 12q^{76} - 96q^{79} - 144q^{81} - 12q^{84} - 48q^{86} - 48q^{89} - 36q^{91} - 216q^{94} - 384q^{99} + O(q^{100})$$

## 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.u.a $$12$$ $$7.586$$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{36}-\zeta_{36}^{7})q^{2}+(-\zeta_{36}^{5}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots$$
950.2.u.b $$12$$ $$7.586$$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots$$
950.2.u.c $$12$$ $$7.586$$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots$$
950.2.u.d $$12$$ $$7.586$$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{36}^{5}q^{2}+(-\zeta_{36}+\zeta_{36}^{3}+\zeta_{36}^{11})q^{3}+\cdots$$
950.2.u.e $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.u.f $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.u.g $$36$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.u.h $$48$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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