# Properties

 Label 605.2.m Level $605$ Weight $2$ Character orbit 605.m Rep. character $\chi_{605}(112,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $368$ Newform subspaces $7$ Sturm bound $132$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.m (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$7$$ Sturm bound: $$132$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(605, [\chi])$$.

Total New Old
Modular forms 624 496 128
Cusp forms 432 368 64
Eisenstein series 192 128 64

## Trace form

 $$368q + 10q^{2} + 2q^{3} + 2q^{5} + 20q^{6} + 10q^{8} + O(q^{10})$$ $$368q + 10q^{2} + 2q^{3} + 2q^{5} + 20q^{6} + 10q^{8} - 124q^{12} + 10q^{13} - 22q^{15} + 40q^{16} + 10q^{18} - 24q^{20} - 64q^{23} - 10q^{25} - 28q^{26} + 14q^{27} - 50q^{28} - 30q^{30} + 28q^{31} + 10q^{35} - 24q^{36} + 14q^{37} - 10q^{38} + 50q^{40} - 40q^{41} - 50q^{42} - 28q^{45} - 60q^{46} + 20q^{47} + 114q^{48} + 50q^{50} - 20q^{51} + 50q^{52} + 44q^{53} - 48q^{56} - 30q^{57} + 26q^{58} - 122q^{60} + 60q^{61} - 100q^{62} + 30q^{63} - 112q^{67} + 30q^{68} - 46q^{70} - 28q^{71} - 80q^{72} - 50q^{73} - 42q^{75} - 236q^{78} + 22q^{80} - 68q^{81} + 14q^{82} - 90q^{83} - 30q^{85} - 108q^{86} + 20q^{90} - 4q^{91} + 40q^{92} + 26q^{93} + 40q^{95} + 14q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(605, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
605.2.m.a $$16$$ $$4.831$$ 16.0.$$\cdots$$.1 $$\Q(\sqrt{-11})$$ $$0$$ $$2$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{4}+\beta _{5})q^{3}+(-2\beta _{5}-2\beta _{7}+\cdots)q^{4}+\cdots$$
605.2.m.b $$16$$ $$4.831$$ $$\Q(\zeta_{40})$$ None $$0$$ $$4$$ $$8$$ $$0$$ $$q+(\zeta_{40}^{9}+\zeta_{40}^{11}+\zeta_{40}^{12}+\zeta_{40}^{15})q^{2}+\cdots$$
605.2.m.c $$32$$ $$4.831$$ None $$0$$ $$6$$ $$-2$$ $$-20$$
605.2.m.d $$32$$ $$4.831$$ None $$0$$ $$6$$ $$-2$$ $$20$$
605.2.m.e $$32$$ $$4.831$$ None $$10$$ $$-4$$ $$-2$$ $$0$$
605.2.m.f $$80$$ $$4.831$$ None $$0$$ $$-4$$ $$-4$$ $$0$$
605.2.m.g $$160$$ $$4.831$$ None $$0$$ $$-8$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(605, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(605, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$