# Properties

 Label 130.2.s Level 130 Weight 2 Character orbit s Rep. character $$\chi_{130}(33,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 28 Newforms 2 Sturm bound 42 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$130 = 2 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 130.s (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$65$$ Character field: $$\Q(\zeta_{12})$$ Newforms: $$2$$ Sturm bound: $$42$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(130, [\chi])$$.

Total New Old
Modular forms 100 28 72
Cusp forms 68 28 40
Eisenstein series 32 0 32

## Trace form

 $$28q + 2q^{2} - 14q^{4} - 4q^{8} + 24q^{9} + O(q^{10})$$ $$28q + 2q^{2} - 14q^{4} - 4q^{8} + 24q^{9} + 12q^{11} - 12q^{13} - 14q^{16} - 2q^{17} - 36q^{19} - 24q^{21} + 26q^{25} - 24q^{27} - 12q^{30} - 24q^{31} + 2q^{32} + 44q^{33} + 26q^{34} - 12q^{35} - 24q^{36} - 18q^{37} - 26q^{41} + 12q^{42} - 12q^{44} - 72q^{45} - 12q^{46} + 2q^{49} + 28q^{50} - 6q^{53} - 32q^{55} + 12q^{56} + 64q^{57} + 12q^{58} + 28q^{59} + 24q^{60} + 24q^{61} + 48q^{62} + 28q^{64} + 66q^{65} + 16q^{66} + 56q^{67} + 4q^{68} - 16q^{69} + 24q^{70} + 24q^{71} + 24q^{72} - 28q^{73} - 30q^{74} + 88q^{75} + 24q^{76} - 88q^{77} + 36q^{78} + 6q^{81} - 28q^{82} - 58q^{85} - 80q^{87} + 18q^{89} + 30q^{90} + 32q^{91} - 36q^{93} - 24q^{94} - 24q^{95} + 20q^{97} - 2q^{98} - 28q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(130, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
130.2.s.a $$12$$ $$1.038$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-6$$ $$0$$ $$0$$ $$6$$ $$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots$$
130.2.s.b $$16$$ $$1.038$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$8$$ $$0$$ $$0$$ $$-6$$ $$q+(1+\beta _{8})q^{2}+(\beta _{2}-\beta _{11})q^{3}+\beta _{8}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(130, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(130, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$