Properties

 Label 130.2.n Level $130$ Weight $2$ Character orbit 130.n Rep. character $\chi_{130}(9,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $1$ Sturm bound $42$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$130 = 2 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 130.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$42$$ Trace bound: $$0$$

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

 $$12q + 6q^{4} - 2q^{9} + O(q^{10})$$ $$12q + 6q^{4} - 2q^{9} - 2q^{10} - 6q^{11} + 20q^{14} + 4q^{15} - 6q^{16} - 26q^{19} - 24q^{21} + 4q^{25} - 28q^{29} - 16q^{30} + 24q^{31} - 16q^{34} - 6q^{35} + 2q^{36} + 36q^{39} - 4q^{40} - 4q^{41} - 12q^{44} + 12q^{45} - 4q^{49} - 8q^{50} + 8q^{51} + 12q^{54} + 12q^{55} + 10q^{56} + 16q^{59} + 8q^{60} - 8q^{61} - 12q^{64} - 10q^{65} - 24q^{66} + 28q^{69} + 24q^{70} + 40q^{71} - 10q^{74} - 8q^{75} + 26q^{76} + 56q^{79} + 26q^{81} - 12q^{84} - 16q^{85} + 24q^{86} + 14q^{89} + 20q^{90} - 38q^{91} - 14q^{94} - 8q^{95} - 52q^{99} + O(q^{100})$$

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.n.a $$12$$ $$1.038$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{5}q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$$

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

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