# 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

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

## 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 $8$ $1.845$ 8.0.$$\cdots$$.5 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

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