# Properties

 Label 130.2.l Level $130$ Weight $2$ Character orbit 130.l Rep. character $\chi_{130}(101,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $2$ 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.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ 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 52 12 40
Cusp forms 36 12 24
Eisenstein series 16 0 16

## Trace form

 $$12q + 6q^{4} - 6q^{9} + O(q^{10})$$ $$12q + 6q^{4} - 6q^{9} + 2q^{10} - 6q^{11} + 12q^{13} - 12q^{14} + 12q^{15} - 6q^{16} - 18q^{19} - 12q^{25} + 24q^{27} + 12q^{29} + 4q^{30} - 60q^{33} - 6q^{35} + 6q^{36} - 12q^{37} - 24q^{38} - 36q^{39} + 4q^{40} - 24q^{41} - 12q^{42} + 12q^{46} + 12q^{49} + 24q^{51} + 48q^{53} + 36q^{54} + 12q^{55} - 6q^{56} + 12q^{58} + 12q^{59} + 24q^{61} + 24q^{62} + 48q^{63} - 12q^{64} + 6q^{65} - 24q^{66} + 24q^{67} + 12q^{69} + 24q^{72} + 18q^{74} - 18q^{76} - 24q^{77} + 12q^{78} + 24q^{79} - 30q^{81} + 12q^{84} - 36q^{85} + 24q^{87} - 42q^{89} - 4q^{90} - 66q^{91} + 36q^{93} + 6q^{94} + 36q^{97} - 48q^{98} + O(q^{100})$$

## 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.l.a $$4$$ $$1.038$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots$$
130.2.l.b $$8$$ $$1.038$$ 8.0.22581504.2 None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(130, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$