# Properties

 Label 335.2.e Level 335 Weight 2 Character orbit e Rep. character $$\chi_{335}(96,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 44 Newforms 2 Sturm bound 68 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$335 = 5 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 335.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$2$$ Sturm bound: $$68$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(335, [\chi])$$.

Total New Old
Modular forms 72 44 28
Cusp forms 64 44 20
Eisenstein series 8 0 8

## Trace form

 $$44q - 6q^{2} - 24q^{4} + 4q^{5} + 4q^{6} - 6q^{7} + 36q^{8} + 24q^{9} + O(q^{10})$$ $$44q - 6q^{2} - 24q^{4} + 4q^{5} + 4q^{6} - 6q^{7} + 36q^{8} + 24q^{9} + 2q^{11} + 2q^{12} + 6q^{13} - 4q^{14} - 44q^{16} + 10q^{17} - 24q^{18} + 2q^{19} - 6q^{20} - 10q^{21} - 8q^{22} - 2q^{23} - 64q^{24} + 44q^{25} + 8q^{26} + 12q^{27} - 16q^{28} + 12q^{29} + 6q^{30} - 42q^{32} + 20q^{33} - 14q^{34} + 2q^{35} - 4q^{36} - 18q^{38} - 38q^{39} - 28q^{41} + 40q^{42} - 24q^{43} + 16q^{44} + 30q^{46} - 2q^{47} + 6q^{48} - 36q^{49} - 6q^{50} + 18q^{51} + 16q^{52} + 16q^{53} - 4q^{55} + 6q^{56} - 70q^{57} - 16q^{59} + 28q^{61} + 32q^{62} - 10q^{63} + 88q^{64} - 4q^{65} + 10q^{67} - 76q^{68} + 10q^{69} - 4q^{70} - 12q^{71} + 144q^{72} + 50q^{73} + 32q^{74} - 36q^{76} + 28q^{77} + 24q^{78} - 28q^{79} + 2q^{80} - 92q^{81} - 32q^{82} - 6q^{83} - 40q^{84} - 2q^{85} + 8q^{86} - 26q^{87} + 14q^{88} + 132q^{89} - 18q^{90} - 64q^{91} + 8q^{92} - 46q^{93} + 44q^{94} - 8q^{95} - 34q^{96} + 42q^{97} - 116q^{98} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(335, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
335.2.e.a $$20$$ $$2.675$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-3$$ $$0$$ $$-20$$ $$-4$$ $$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(\beta _{10}-\beta _{18})q^{4}+\cdots$$
335.2.e.b $$24$$ $$2.675$$ None $$-3$$ $$0$$ $$24$$ $$-2$$

## Decomposition of $$S_{2}^{\mathrm{old}}(335, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(335, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 2}$$