# Properties

 Label 605.2.s Level $605$ Weight $2$ Character orbit 605.s Rep. character $\chi_{605}(16,\cdot)$ Character field $\Q(\zeta_{55})$ Dimension $1760$ Newform subspaces $2$ Sturm bound $132$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.s (of order $$55$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{55})$$ Newform subspaces: $$2$$ Sturm bound: $$132$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 2720 1760 960
Cusp forms 2560 1760 800
Eisenstein series 160 0 160

## Trace form

 $$1760q + 6q^{2} + 4q^{3} + 48q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 434q^{9} + O(q^{10})$$ $$1760q + 6q^{2} + 4q^{3} + 48q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 434q^{9} - 8q^{10} + 2q^{11} - 54q^{12} - 24q^{13} - 48q^{14} - 28q^{15} + 52q^{16} + 12q^{17} - 14q^{18} - 14q^{19} + 32q^{21} - 26q^{22} - 20q^{23} - 126q^{24} + 44q^{25} - 4q^{26} - 20q^{27} + 2q^{28} - 10q^{29} + 20q^{30} - 44q^{31} - 28q^{32} + 14q^{33} + 64q^{34} + 12q^{35} + 14q^{36} - 36q^{37} - 18q^{38} - 30q^{39} - 60q^{40} - 4q^{41} - 66q^{42} - 4q^{43} + 18q^{44} + 38q^{46} - 12q^{47} - 6q^{48} - 2q^{49} + 6q^{50} - 124q^{51} - 254q^{52} - 240q^{53} - 130q^{54} - 12q^{55} + 54q^{56} - 104q^{57} - 216q^{58} + 34q^{59} - 26q^{60} - 4q^{61} - 42q^{62} - 26q^{63} - 168q^{64} - 16q^{65} - 48q^{66} + 34q^{67} - 46q^{68} + 14q^{69} - 36q^{70} - 32q^{71} + 64q^{72} - 34q^{73} - 68q^{74} - 6q^{75} - 280q^{76} - 270q^{77} - 72q^{78} - 186q^{79} - 24q^{80} - 468q^{81} - 126q^{82} - 2q^{83} - 24q^{84} - 50q^{85} + 10q^{86} - 68q^{87} - 228q^{88} - 8q^{89} - 62q^{90} - 188q^{91} - 388q^{92} - 50q^{93} - 138q^{94} + 16q^{95} - 270q^{96} - 138q^{97} - 284q^{98} + 16q^{99} + O(q^{100})$$

## 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.s.a $$880$$ $$4.831$$ None $$2$$ $$5$$ $$-22$$ $$1$$
605.2.s.b $$880$$ $$4.831$$ None $$4$$ $$-1$$ $$22$$ $$3$$

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

$$S_{2}^{\mathrm{old}}(605, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$