# Properties

 Label 130.2.j Level $130$ Weight $2$ Character orbit 130.j Rep. character $\chi_{130}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $14$ Newform subspaces $5$ 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: $$\Q(i)$$ Newform subspaces: $$5$$ 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

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

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

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

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