# Properties

 Label 130.2.j Level 130 Weight 2 Character orbit j Rep. character $$\chi_{130}(47,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 14 Newforms 5 Sturm bound 42 Trace bound 5

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 50 14 36
Cusp forms 34 14 20
Eisenstein series 16 0 16

## Trace form

 $$14q - 14q^{4} + 2q^{5} + O(q^{10})$$ $$14q - 14q^{4} + 2q^{5} - 12q^{11} - 14q^{13} + 14q^{16} - 2q^{17} - 26q^{18} + 12q^{19} - 2q^{20} + 24q^{21} + 24q^{23} + 2q^{25} - 12q^{27} + 24q^{30} - 24q^{31} + 2q^{34} + 12q^{35} + 32q^{37} - 22q^{41} - 12q^{42} - 24q^{43} + 12q^{44} - 12q^{45} - 12q^{46} - 64q^{47} - 10q^{49} + 14q^{52} + 30q^{53} + 8q^{55} + 28q^{58} - 20q^{59} + 12q^{62} - 14q^{64} + 10q^{65} + 32q^{66} + 2q^{68} + 32q^{69} + 44q^{70} + 26q^{72} - 56q^{75} - 12q^{76} + 8q^{77} - 32q^{78} + 2q^{80} + 18q^{81} - 34q^{82} - 8q^{83} - 24q^{84} + 2q^{85} - 16q^{87} - 6q^{89} + 30q^{90} - 32q^{91} - 24q^{92} + 32q^{93} + 24q^{95} + 44q^{99} + O(q^{100})$$

## 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.j.a $$2$$ $$1.038$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$-2$$ $$-8$$ $$q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$$
130.2.j.b $$2$$ $$1.038$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$-4$$ $$q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots$$
130.2.j.c $$2$$ $$1.038$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$-4$$ $$q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots$$
130.2.j.d $$4$$ $$1.038$$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$2$$ $$0$$ $$12$$ $$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots$$
130.2.j.e $$4$$ $$1.038$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$4$$ $$4$$ $$q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$$

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

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