# Properties

 Label 605.2.k Level $605$ Weight $2$ Character orbit 605.k Rep. character $\chi_{605}(56,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $440$ 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.k (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{11})$$ 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 680 440 240
Cusp forms 640 440 200
Eisenstein series 40 0 40

## Trace form

 $$440q - 6q^{2} - 4q^{3} - 48q^{4} - 4q^{6} - 4q^{7} - 18q^{8} + 424q^{9} + O(q^{10})$$ $$440q - 6q^{2} - 4q^{3} - 48q^{4} - 4q^{6} - 4q^{7} - 18q^{8} + 424q^{9} - 2q^{10} - 12q^{11} + 54q^{12} + 14q^{13} + 28q^{14} + 18q^{15} - 72q^{16} - 32q^{17} - 46q^{18} - 16q^{19} - 32q^{21} - 34q^{22} + 20q^{23} + 36q^{24} - 44q^{25} - 36q^{26} - 40q^{27} - 52q^{28} - 40q^{29} - 20q^{30} + 24q^{31} - 62q^{32} - 44q^{33} - 64q^{34} - 12q^{35} - 124q^{36} - 24q^{37} - 32q^{38} - 40q^{39} + 60q^{40} - 56q^{41} - 84q^{42} - 36q^{43} - 58q^{44} - 68q^{46} - 28q^{47} - 104q^{48} - 28q^{49} - 6q^{50} + 54q^{51} + 204q^{52} + 160q^{53} + 50q^{54} - 8q^{55} - 54q^{56} + 74q^{57} + 126q^{58} - 44q^{59} - 44q^{60} - 56q^{61} + 22q^{62} - 84q^{63} + 68q^{64} - 24q^{65} - 102q^{66} - 34q^{67} - 144q^{68} - 104q^{69} - 24q^{70} - 68q^{71} - 234q^{72} - 36q^{73} - 92q^{74} - 4q^{75} + 120q^{76} + 180q^{77} + 72q^{78} + 36q^{79} - 16q^{80} + 328q^{81} - 44q^{82} - 68q^{83} - 256q^{84} + 50q^{85} - 100q^{86} - 152q^{87} + 68q^{88} + 8q^{89} + 62q^{90} + 28q^{91} + 148q^{92} - 30q^{93} - 52q^{94} - 16q^{95} + 20q^{96} - 2q^{97} + 194q^{98} - 156q^{99} + O(q^{100})$$

## 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.k.a $$220$$ $$4.831$$ None $$-4$$ $$-4$$ $$-22$$ $$-8$$
605.2.k.b $$220$$ $$4.831$$ None $$-2$$ $$0$$ $$22$$ $$4$$

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

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