# Properties

 Label 950.2.l Level $950$ Weight $2$ Character orbit 950.l Rep. character $\chi_{950}(101,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $186$ Newform subspaces $13$ Sturm bound $300$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.l (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$13$$ Sturm bound: $$300$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 972 186 786
Cusp forms 828 186 642
Eisenstein series 144 0 144

## Trace form

 $$186q - 3q^{3} - 3q^{6} + 6q^{7} - 3q^{8} - 3q^{9} + O(q^{10})$$ $$186q - 3q^{3} - 3q^{6} + 6q^{7} - 3q^{8} - 3q^{9} + 6q^{11} + 12q^{13} - 12q^{14} + 24q^{17} + 42q^{18} + 42q^{19} + 48q^{21} + 24q^{22} + 36q^{23} - 3q^{24} - 6q^{26} + 3q^{27} - 6q^{28} + 6q^{29} + 6q^{31} - 45q^{33} - 12q^{34} - 3q^{36} - 12q^{37} - 9q^{38} + 84q^{39} + 15q^{41} - 12q^{42} - 30q^{43} + 12q^{44} + 54q^{47} + 6q^{48} - 45q^{49} - 69q^{51} - 6q^{52} + 60q^{53} + 45q^{54} - 36q^{56} + 108q^{57} + 24q^{58} + 51q^{59} - 102q^{61} + 42q^{62} + 48q^{63} - 93q^{64} - 63q^{66} - 9q^{67} + 9q^{68} + 42q^{69} - 18q^{71} + 6q^{72} + 6q^{73} + 18q^{74} + 6q^{76} - 60q^{77} - 18q^{78} + 6q^{79} + 15q^{81} - 45q^{82} - 30q^{83} - 6q^{84} - 36q^{86} - 102q^{87} - 6q^{88} - 96q^{89} - 48q^{91} - 18q^{92} - 78q^{93} + 12q^{94} - 21q^{97} - 24q^{98} + 21q^{99} + O(q^{100})$$

## 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.l.a $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}^{2})q^{3}+\cdots$$
950.2.l.b $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$-3$$ $$0$$ $$-3$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}+\cdots)q^{3}+\cdots$$
950.2.l.c $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
950.2.l.d $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$0$$ $$6$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
950.2.l.e $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$0$$ $$3$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
950.2.l.f $$6$$ $$7.586$$ $$\Q(\zeta_{18})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots$$
950.2.l.g $$12$$ $$7.586$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-3$$ $$0$$ $$6$$ $$q+\beta _{8}q^{2}+\beta _{4}q^{3}+\beta _{10}q^{4}+(\beta _{6}-\beta _{8}+\cdots)q^{6}+\cdots$$
950.2.l.h $$12$$ $$7.586$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{7}q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{6}+\cdots$$
950.2.l.i $$18$$ $$7.586$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{5}q^{6}+\cdots$$
950.2.l.j $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$-3$$
950.2.l.k $$24$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$3$$
950.2.l.l $$30$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$-12$$
950.2.l.m $$30$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$12$$

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

$$S_{2}^{\mathrm{old}}(950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$