# Properties

 Label 930.2.be Level $930$ Weight $2$ Character orbit 930.be Rep. character $\chi_{930}(37,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $128$ Newform subspaces $2$ Sturm bound $384$ Trace bound $7$

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## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.be (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$7$$ 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

 $$128q - 4q^{7} + O(q^{10})$$ $$128q - 4q^{7} - 8q^{10} - 128q^{16} - 48q^{21} - 12q^{22} + 8q^{25} + 4q^{28} + 16q^{31} + 8q^{33} + 48q^{35} + 64q^{36} + 72q^{37} - 32q^{38} - 16q^{41} + 12q^{42} - 96q^{43} + 16q^{47} - 16q^{50} + 60q^{55} - 24q^{57} + 16q^{62} - 8q^{63} + 144q^{65} + 16q^{66} + 32q^{67} - 88q^{70} + 16q^{71} - 48q^{73} - 16q^{76} + 64q^{81} + 16q^{82} - 24q^{83} - 48q^{86} - 52q^{87} + 12q^{88} + 24q^{93} + 128q^{95} - 136q^{97} - 32q^{98} + O(q^{100})$$

## 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.be.a $$64$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$-8$$
930.2.be.b $$64$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

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