Properties

 Label 950.2.f Level $950$ Weight $2$ Character orbit 950.f Rep. character $\chi_{950}(493,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $60$ Newform subspaces $4$ 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.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ 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 324 60 264
Cusp forms 276 60 216
Eisenstein series 48 0 48

Trace form

 $$60q - 4q^{7} + O(q^{10})$$ $$60q - 4q^{7} - 16q^{11} - 60q^{16} + 20q^{17} + 4q^{23} + 16q^{26} - 4q^{28} + 60q^{36} + 4q^{38} + 32q^{42} - 4q^{43} - 60q^{47} + 48q^{57} - 16q^{61} - 16q^{62} + 28q^{63} + 88q^{66} + 20q^{68} - 12q^{73} - 64q^{77} - 60q^{81} - 16q^{82} - 20q^{83} + 8q^{87} - 4q^{92} - 104q^{93} + O(q^{100})$$

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.f.a $$4$$ $$7.586$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots$$
950.2.f.b $$8$$ $$7.586$$ 8.0.3317760000.4 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+q^{6}+\beta _{3}q^{7}+\cdots$$
950.2.f.c $$16$$ $$7.586$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{9}q^{2}+\beta _{13}q^{3}+\beta _{1}q^{4}+\beta _{2}q^{6}+\cdots$$
950.2.f.d $$32$$ $$7.586$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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