# Properties

 Label 130.2.c Level $130$ Weight $2$ Character orbit 130.c Rep. character $\chi_{130}(129,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $42$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$130 = 2 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 130.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$42$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

## Trace form

 $$8 q + 8 q^{4} - 4 q^{9} + O(q^{10})$$ $$8 q + 8 q^{4} - 4 q^{9} - 6 q^{10} - 4 q^{14} + 8 q^{16} + 2 q^{25} - 8 q^{26} - 24 q^{29} - 2 q^{30} - 30 q^{35} - 4 q^{36} - 24 q^{39} - 6 q^{40} + 12 q^{49} + 52 q^{51} + 40 q^{55} - 4 q^{56} - 8 q^{61} + 8 q^{64} + 6 q^{65} + 32 q^{66} + 88 q^{69} - 4 q^{74} - 30 q^{75} - 8 q^{79} - 16 q^{81} + 36 q^{90} + 4 q^{91} - 60 q^{94} - 36 q^{95} + O(q^{100})$$

## 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.c.a $4$ $1.038$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-4$$ $$0$$ $$3$$ $$2$$ $$q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots$$
130.2.c.b $4$ $1.038$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$4$$ $$0$$ $$-3$$ $$-2$$ $$q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots$$

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

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