# Properties

 Label 930.2.n Level $930$ Weight $2$ Character orbit 930.n Rep. character $\chi_{930}(481,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $96$ Newform subspaces $8$ Sturm bound $384$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.n (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$31$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$8$$ Sturm bound: $$384$$ Trace bound: $$3$$ 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 96 704
Cusp forms 736 96 640
Eisenstein series 64 0 64

## Trace form

 $$96q - 4q^{3} - 24q^{4} - 8q^{7} - 24q^{9} + O(q^{10})$$ $$96q - 4q^{3} - 24q^{4} - 8q^{7} - 24q^{9} + 24q^{11} - 4q^{12} + 8q^{13} + 24q^{14} - 24q^{16} + 8q^{17} - 8q^{19} + 12q^{21} - 24q^{22} + 8q^{23} + 96q^{25} + 64q^{26} - 4q^{27} + 12q^{28} + 8q^{29} + 16q^{30} + 40q^{31} + 24q^{33} + 12q^{34} + 24q^{35} + 96q^{36} - 8q^{37} + 32q^{38} + 28q^{39} + 32q^{41} - 8q^{42} - 4q^{43} - 16q^{44} - 20q^{46} - 32q^{47} - 4q^{48} + 8q^{51} + 8q^{52} - 8q^{53} + 12q^{55} - 16q^{56} + 8q^{57} - 16q^{58} + 32q^{59} + 24q^{61} - 24q^{62} - 8q^{63} - 24q^{64} - 4q^{66} + 8q^{67} - 32q^{68} + 8q^{71} + 8q^{73} - 8q^{74} - 4q^{75} + 12q^{76} - 24q^{77} + 24q^{78} + 32q^{79} - 24q^{81} - 8q^{82} - 32q^{83} - 8q^{84} + 16q^{85} - 8q^{86} - 16q^{87} + 16q^{88} - 24q^{89} + 76q^{91} - 32q^{92} - 36q^{93} - 24q^{94} + 20q^{97} - 32q^{98} - 16q^{99} + O(q^{100})$$

## 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.n.a $$8$$ $$7.426$$ 8.0.13140625.1 None $$-2$$ $$2$$ $$8$$ $$9$$ $$q-\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{4}q^{4}+q^{5}-q^{6}+\cdots$$
930.2.n.b $$8$$ $$7.426$$ 8.0.1816890625.5 None $$2$$ $$2$$ $$-8$$ $$-7$$ $$q-\beta _{2}q^{2}+\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
930.2.n.c $$12$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-3$$ $$-3$$ $$-12$$ $$-1$$ $$q-\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{8}q^{4}-q^{5}+q^{6}+\cdots$$
930.2.n.d $$12$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-3$$ $$3$$ $$-12$$ $$-1$$ $$q+(-1-\beta _{3}+\beta _{5}-\beta _{6})q^{2}+\beta _{5}q^{3}+\cdots$$
930.2.n.e $$12$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$3$$ $$-3$$ $$12$$ $$-1$$ $$q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-1-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$$
930.2.n.f $$12$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$3$$ $$3$$ $$12$$ $$-1$$ $$q+\beta _{8}q^{2}-\beta _{6}q^{3}+(-1-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$$
930.2.n.g $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-4$$ $$-4$$ $$16$$ $$1$$ $$q+\beta _{6}q^{2}-\beta _{7}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$$
930.2.n.h $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$4$$ $$-4$$ $$-16$$ $$-7$$ $$q+\beta _{7}q^{2}+\beta _{3}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(62, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(93, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(186, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(310, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$