# Properties

 Label 363.2.i Level 363 Weight 2 Character orbit i Rep. character $$\chi_{363}(34,\cdot)$$ Character field $$\Q(\zeta_{11})$$ Dimension 220 Newform subspaces 2 Sturm bound 88 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 363.i (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$121$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$2$$ Sturm bound: $$88$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(363, [\chi])$$.

Total New Old
Modular forms 460 220 240
Cusp forms 420 220 200
Eisenstein series 40 0 40

## Trace form

 $$220q - 4q^{2} - 26q^{4} - 4q^{5} - 2q^{6} - 12q^{7} - 12q^{8} + 220q^{9} + O(q^{10})$$ $$220q - 4q^{2} - 26q^{4} - 4q^{5} - 2q^{6} - 12q^{7} - 12q^{8} + 220q^{9} + 6q^{10} + 10q^{11} - 8q^{12} + 32q^{13} + 24q^{14} - 8q^{15} - 42q^{16} - 16q^{17} - 4q^{18} - 20q^{19} - 36q^{20} - 4q^{21} + 10q^{22} + 16q^{23} - 18q^{24} - 50q^{25} - 28q^{26} - 52q^{28} - 24q^{29} - 20q^{30} + 2q^{31} - 68q^{32} - 10q^{33} - 40q^{34} - 40q^{35} - 26q^{36} + 26q^{37} - 56q^{38} - 16q^{39} + 36q^{40} - 40q^{41} - 16q^{42} - 44q^{43} - 54q^{44} - 4q^{45} - 80q^{46} - 48q^{47} - 32q^{48} - 34q^{49} + 172q^{50} - 20q^{51} + 54q^{52} + 76q^{53} - 2q^{54} + 24q^{55} + 70q^{56} - 20q^{57} + 2q^{58} - 36q^{59} - 28q^{60} - 68q^{61} + 22q^{62} - 12q^{63} - 82q^{64} - 22q^{65} - 32q^{66} + 58q^{67} - 128q^{68} - 12q^{69} - 64q^{70} + 36q^{71} - 12q^{72} - 38q^{73} - 120q^{74} - 24q^{75} + 102q^{76} - 92q^{77} + 78q^{78} + 56q^{79} - 152q^{80} + 220q^{81} - 48q^{82} - 96q^{83} - 60q^{84} - 24q^{85} - 100q^{86} - 36q^{87} - 118q^{88} + 20q^{89} + 6q^{90} - 6q^{91} + 92q^{92} - 32q^{93} + 200q^{94} - 120q^{95} + 74q^{96} - 10q^{97} - 4q^{98} + 10q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(363, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
363.2.i.a $$110$$ $$2.899$$ None $$-3$$ $$110$$ $$-6$$ $$-8$$
363.2.i.b $$110$$ $$2.899$$ None $$-1$$ $$-110$$ $$2$$ $$-4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(363, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(363, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database