# Properties

 Label 950.2.bb Level $950$ Weight $2$ Character orbit 950.bb Rep. character $\chi_{950}(143,\cdot)$ Character field $\Q(\zeta_{36})$ Dimension $360$ Newform subspaces $5$ Sturm bound $300$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.bb (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{36})$$ Newform subspaces: $$5$$ Sturm bound: $$300$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 1944 360 1584
Cusp forms 1656 360 1296
Eisenstein series 288 0 288

## Trace form

 $$360q + 12q^{7} + O(q^{10})$$ $$360q + 12q^{7} - 36q^{17} - 48q^{21} - 24q^{22} + 24q^{26} + 96q^{33} + 24q^{41} + 72q^{43} + 24q^{47} + 132q^{51} - 36q^{53} - 84q^{57} + 24q^{61} + 24q^{62} - 36q^{63} - 132q^{66} + 96q^{67} + 12q^{68} + 36q^{73} - 24q^{76} - 96q^{78} - 288q^{81} - 48q^{82} - 24q^{83} - 96q^{86} - 72q^{87} - 24q^{91} - 72q^{92} - 156q^{93} - 120q^{97} - 24q^{98} + O(q^{100})$$

## 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.bb.a $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.bb.b $$48$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.bb.c $$72$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.bb.d $$96$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$
950.2.bb.e $$120$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$12$$

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

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