# Properties

 Label 637.2.q Level $637$ Weight $2$ Character orbit 637.q Rep. character $\chi_{637}(491,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $86$ Newform subspaces $10$ Sturm bound $130$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$130$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(637, [\chi])$$.

Total New Old
Modular forms 148 106 42
Cusp forms 116 86 30
Eisenstein series 32 20 12

## Trace form

 $$86q + 3q^{2} + 2q^{3} + 39q^{4} + 12q^{6} - 35q^{9} + O(q^{10})$$ $$86q + 3q^{2} + 2q^{3} + 39q^{4} + 12q^{6} - 35q^{9} - 9q^{10} - 6q^{11} + 8q^{12} + q^{13} - 36q^{15} - 29q^{16} + q^{17} + 6q^{19} + 9q^{20} - 12q^{22} + 4q^{23} - 6q^{24} - 40q^{25} + 39q^{26} - 4q^{27} - 11q^{29} + 38q^{30} - 27q^{32} + 30q^{33} + 31q^{36} - 15q^{37} - 16q^{38} - 6q^{39} - 98q^{40} - 21q^{41} - 16q^{43} + 3q^{45} - 6q^{46} - 8q^{48} + 78q^{50} + 12q^{51} - 4q^{52} + 14q^{53} - 24q^{54} + 6q^{55} - 93q^{58} - 30q^{59} - 13q^{61} - 2q^{62} + 38q^{64} + 11q^{65} + 52q^{66} + 42q^{67} + 11q^{68} - 16q^{69} - 24q^{71} + 45q^{72} - 21q^{74} - 42q^{75} + 24q^{76} - 42q^{78} + 96q^{79} + 87q^{80} - 23q^{81} - 23q^{82} + 27q^{85} + 8q^{87} + 38q^{88} + 24q^{89} - 30q^{90} - 40q^{92} + 60q^{93} + 2q^{94} + 56q^{95} - 18q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(637, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
637.2.q.a $$2$$ $$5.086$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$2$$ $$0$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
637.2.q.b $$2$$ $$5.086$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$-1$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
637.2.q.c $$2$$ $$5.086$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$1$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
637.2.q.d $$4$$ $$5.086$$ $$\Q(\sqrt{-3}, \sqrt{-13})$$ None $$-6$$ $$0$$ $$0$$ $$0$$ $$q+(-2+\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$$
637.2.q.e $$4$$ $$5.086$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$3$$ $$-1$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$$
637.2.q.f $$4$$ $$5.086$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$3$$ $$1$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$$
637.2.q.g $$12$$ $$5.086$$ 12.0.$$\cdots$$.1 None $$0$$ $$-3$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
637.2.q.h $$12$$ $$5.086$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$$
637.2.q.i $$12$$ $$5.086$$ 12.0.$$\cdots$$.1 None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
637.2.q.j $$32$$ $$5.086$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(637, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(637, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$