# Properties

 Label 930.2.z Level $930$ Weight $2$ Character orbit 930.z Rep. character $\chi_{930}(109,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $128$ Newform subspaces $4$ Sturm bound $384$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.z (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 800 128 672
Cusp forms 736 128 608
Eisenstein series 64 0 64

## Trace form

 $$128q + 32q^{4} + 16q^{6} + 32q^{9} + O(q^{10})$$ $$128q + 32q^{4} + 16q^{6} + 32q^{9} + 4q^{10} + 4q^{15} - 32q^{16} - 16q^{19} - 32q^{21} + 4q^{24} - 12q^{25} + 56q^{29} + 8q^{30} + 16q^{31} + 28q^{34} - 8q^{35} + 128q^{36} + 16q^{39} + 6q^{40} - 72q^{41} - 44q^{46} + 28q^{49} - 40q^{50} + 4q^{54} - 64q^{59} - 4q^{60} + 112q^{61} + 32q^{64} + 44q^{65} - 12q^{66} + 56q^{70} - 40q^{71} + 24q^{75} - 24q^{76} + 108q^{79} - 32q^{81} - 8q^{84} - 44q^{85} + 88q^{86} - 88q^{89} - 4q^{90} - 24q^{94} + 44q^{95} - 4q^{96} + O(q^{100})$$

## 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.z.a $$8$$ $$7.426$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots$$
930.2.z.b $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q-\beta _{12}q^{2}-\beta _{14}q^{3}-\beta _{15}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$$
930.2.z.c $$32$$ $$7.426$$ None $$0$$ $$0$$ $$-16$$ $$0$$
930.2.z.d $$72$$ $$7.426$$ None $$0$$ $$0$$ $$4$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(310, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$