Properties

 Label 930.2.bg Level $930$ Weight $2$ Character orbit 930.bg Rep. character $\chi_{930}(121,\cdot)$ Character field $\Q(\zeta_{15})$ Dimension $160$ Newform subspaces $9$ Sturm bound $384$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.bg (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$31$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$9$$ Sturm bound: $$384$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$

Dimensions

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

Total New Old
Modular forms 1600 160 1440
Cusp forms 1472 160 1312
Eisenstein series 128 0 128

Trace form

 $$160q - 40q^{4} + 20q^{9} + O(q^{10})$$ $$160q - 40q^{4} + 20q^{9} - 48q^{11} - 16q^{13} - 48q^{14} - 40q^{16} - 32q^{17} + 16q^{23} - 80q^{25} + 32q^{26} + 64q^{29} + 32q^{30} + 40q^{31} + 48q^{33} + 36q^{34} + 48q^{35} - 80q^{36} - 48q^{37} + 16q^{38} - 40q^{39} + 40q^{41} + 8q^{42} - 8q^{43} - 8q^{44} - 28q^{46} - 16q^{47} + 60q^{49} - 56q^{51} - 16q^{52} + 56q^{53} - 24q^{55} - 8q^{56} - 16q^{57} - 56q^{58} + 40q^{59} - 80q^{61} - 40q^{64} + 4q^{66} + 56q^{67} + 8q^{68} - 56q^{71} + 56q^{73} - 16q^{74} + 96q^{77} - 24q^{78} + 40q^{79} + 20q^{81} + 56q^{82} + 8q^{83} - 40q^{85} - 40q^{86} - 8q^{87} - 40q^{88} - 72q^{89} + 72q^{91} - 64q^{92} + 8q^{93} + 24q^{94} + 112q^{97} + 32q^{98} - 8q^{99} + O(q^{100})$$

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.bg.a $$8$$ $$7.426$$ $$\Q(\zeta_{15})$$ None $$-2$$ $$-1$$ $$4$$ $$2$$ $$q+\zeta_{15}^{3}q^{2}-\zeta_{15}^{7}q^{3}+\zeta_{15}^{6}q^{4}+\cdots$$
930.2.bg.b $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-4$$ $$-2$$ $$-8$$ $$3$$ $$q-\beta _{5}q^{2}+\beta _{10}q^{3}+(-1+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$$
930.2.bg.c $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-4$$ $$-2$$ $$8$$ $$11$$ $$q+(\beta _{4}+\beta _{7}+\beta _{8}+\beta _{9}-\beta _{10})q^{2}+\beta _{10}q^{3}+\cdots$$
930.2.bg.d $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-4$$ $$2$$ $$8$$ $$11$$ $$q+\beta _{4}q^{2}+(\beta _{5}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
930.2.bg.e $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$4$$ $$-2$$ $$8$$ $$-5$$ $$q+\beta _{9}q^{2}+(-1+\beta _{3}+\beta _{4}-\beta _{6}+\beta _{9}+\cdots)q^{3}+\cdots$$
930.2.bg.f $$16$$ $$7.426$$ 16.0.$$\cdots$$.1 None $$4$$ $$2$$ $$-8$$ $$-13$$ $$q+(1-\beta _{11}-\beta _{13}+\beta _{15})q^{2}+(-\beta _{3}+\cdots)q^{3}+\cdots$$
930.2.bg.g $$24$$ $$7.426$$ None $$-6$$ $$3$$ $$-12$$ $$9$$
930.2.bg.h $$24$$ $$7.426$$ None $$6$$ $$-3$$ $$-12$$ $$-11$$
930.2.bg.i $$24$$ $$7.426$$ None $$6$$ $$3$$ $$12$$ $$-7$$

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

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