# Properties

 Label 231.2.i Level $231$ Weight $2$ Character orbit 231.i Rep. character $\chi_{231}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $28$ Newform subspaces $6$ Sturm bound $64$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$231 = 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 231.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$64$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(231, [\chi])$$.

Total New Old
Modular forms 72 28 44
Cusp forms 56 28 28
Eisenstein series 16 0 16

## Trace form

 $$28q + 2q^{3} - 16q^{4} + 2q^{7} + 24q^{8} - 14q^{9} + O(q^{10})$$ $$28q + 2q^{3} - 16q^{4} + 2q^{7} + 24q^{8} - 14q^{9} - 12q^{10} + 4q^{12} + 12q^{13} - 4q^{14} - 28q^{16} - 6q^{19} - 32q^{20} - 8q^{21} + 8q^{23} - 10q^{25} - 4q^{26} - 4q^{27} - 8q^{28} - 16q^{30} + 22q^{31} - 44q^{32} + 4q^{33} + 24q^{34} + 48q^{35} + 32q^{36} - 2q^{37} + 12q^{38} + 2q^{39} - 12q^{40} - 32q^{41} + 12q^{42} - 12q^{43} - 8q^{44} - 32q^{46} - 28q^{47} + 16q^{48} + 22q^{49} + 64q^{50} + 8q^{51} - 8q^{52} + 36q^{53} - 32q^{55} + 24q^{56} + 12q^{57} + 4q^{58} - 32q^{59} - 8q^{60} + 8q^{61} - 88q^{62} + 2q^{63} + 88q^{64} + 40q^{65} + 8q^{66} - 22q^{67} + 36q^{68} - 24q^{69} + 24q^{70} + 16q^{71} - 12q^{72} - 30q^{73} + 48q^{74} + 6q^{75} + 120q^{76} + 4q^{77} - 8q^{78} + 14q^{79} - 16q^{80} - 14q^{81} - 32q^{83} - 52q^{84} + 8q^{85} - 36q^{86} - 12q^{87} + 12q^{88} - 20q^{89} + 24q^{90} - 10q^{91} + 80q^{92} + 2q^{93} - 52q^{94} + 16q^{95} - 20q^{96} - 128q^{97} + 12q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(231, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
231.2.i.a $$2$$ $$1.845$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
231.2.i.b $$2$$ $$1.845$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-4$$ $$-4$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
231.2.i.c $$2$$ $$1.845$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$1$$ $$0$$ $$5$$ $$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
231.2.i.d $$4$$ $$1.845$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$-2$$ $$4$$ $$4$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
231.2.i.e $$8$$ $$1.845$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-2$$ $$-4$$ $$-4$$ $$2$$ $$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
231.2.i.f $$10$$ $$1.845$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-2$$ $$5$$ $$4$$ $$-1$$ $$q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(231, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(231, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 2}$$