# Properties

 Label 930.2.y Level $930$ Weight $2$ Character orbit 930.y Rep. character $\chi_{930}(29,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $256$ Newform subspaces $2$ Sturm bound $384$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.y (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$465$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(930, [\chi])$$.

Total New Old
Modular forms 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

## Trace form

 $$256q - 64q^{4} - 8q^{9} + O(q^{10})$$ $$256q - 64q^{4} - 8q^{9} + 4q^{10} - 10q^{15} - 64q^{16} - 16q^{19} - 20q^{25} - 96q^{31} + 20q^{34} - 8q^{36} + 8q^{39} - 6q^{40} + 42q^{45} + 20q^{46} + 92q^{49} + 68q^{51} + 10q^{60} - 64q^{64} - 16q^{66} + 16q^{69} + 32q^{70} + 10q^{75} + 24q^{76} - 20q^{79} - 48q^{81} - 60q^{85} - 58q^{90} + 40q^{91} - 8q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(930, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
930.2.y.a $$128$$ $$7.426$$ None $$-32$$ $$0$$ $$2$$ $$0$$
930.2.y.b $$128$$ $$7.426$$ None $$32$$ $$0$$ $$-2$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(930, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$