# Properties

 Label 650.2.m Level $650$ Weight $2$ Character orbit 650.m Rep. character $\chi_{650}(101,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $5$ Sturm bound $210$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$650 = 2 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 650.m (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$210$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(650, [\chi])$$.

Total New Old
Modular forms 236 44 192
Cusp forms 188 44 144
Eisenstein series 48 0 48

## Trace form

 $$44q + 22q^{4} - 18q^{9} + O(q^{10})$$ $$44q + 22q^{4} - 18q^{9} + 12q^{11} - 12q^{13} + 8q^{14} - 22q^{16} - 24q^{19} + 14q^{26} - 24q^{27} - 6q^{29} + 60q^{33} + 18q^{36} + 12q^{37} + 24q^{38} + 4q^{39} - 30q^{41} + 12q^{42} - 24q^{46} + 22q^{49} - 16q^{51} - 48q^{53} - 36q^{54} + 4q^{56} - 12q^{58} + 12q^{59} - 6q^{61} - 24q^{62} - 48q^{63} - 44q^{64} + 16q^{66} - 24q^{67} - 20q^{69} - 24q^{72} - 22q^{74} - 24q^{76} + 24q^{77} - 12q^{78} + 8q^{79} + 2q^{81} + 36q^{84} - 24q^{87} + 24q^{89} + 20q^{91} - 36q^{93} - 12q^{94} - 36q^{97} + 48q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(650, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
650.2.m.a $$4$$ $$5.190$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots$$
650.2.m.b $$8$$ $$5.190$$ 8.0.22581504.2 None $$0$$ $$-2$$ $$0$$ $$-6$$ $$q-\beta _{7}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$$
650.2.m.c $$8$$ $$5.190$$ 8.0.22581504.2 None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$$
650.2.m.d $$8$$ $$5.190$$ 8.0.22581504.2 None $$0$$ $$2$$ $$0$$ $$6$$ $$q+\beta _{7}q^{2}+(2-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$$
650.2.m.e $$16$$ $$5.190$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{6})q^{2}-\beta _{5}q^{3}-\beta _{8}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(650, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(650, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 2}$$