# Properties

 Label 231.2.s Level 231 Weight 2 Character orbit s Rep. character $$\chi_{231}(8,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 96 Newform subspaces 1 Sturm bound 64 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$231 = 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 231.s (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$33$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 144 96 48
Cusp forms 112 96 16
Eisenstein series 32 0 32

## Trace form

 $$96q + 6q^{3} - 24q^{4} - 10q^{6} - 20q^{9} + O(q^{10})$$ $$96q + 6q^{3} - 24q^{4} - 10q^{6} - 20q^{9} - 20q^{12} - 32q^{16} - 10q^{18} - 60q^{19} + 30q^{24} + 12q^{25} - 40q^{28} + 60q^{30} + 40q^{31} - 44q^{33} + 8q^{34} + 2q^{36} + 16q^{37} - 10q^{39} - 96q^{45} - 40q^{46} + 48q^{48} + 24q^{49} - 30q^{51} - 40q^{52} + 28q^{55} - 30q^{57} + 36q^{58} - 32q^{60} + 40q^{61} - 28q^{64} + 118q^{66} - 56q^{67} + 26q^{69} + 20q^{70} + 150q^{72} + 40q^{73} + 2q^{75} - 20q^{78} - 40q^{79} + 8q^{81} - 16q^{82} + 40q^{84} - 60q^{85} - 156q^{88} + 100q^{90} + 36q^{91} - 36q^{93} + 160q^{96} - 88q^{97} - 94q^{99} + O(q^{100})$$

## 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.s.a $$96$$ $$1.845$$ None $$0$$ $$6$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(231, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database