# Properties

 Label 228.2.p Level $228$ Weight $2$ Character orbit 228.p Rep. character $\chi_{228}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $4$ Sturm bound $80$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 228.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$80$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(228, [\chi])$$.

Total New Old
Modular forms 92 12 80
Cusp forms 68 12 56
Eisenstein series 24 0 24

## Trace form

 $$12 q - 3 q^{3} - 4 q^{7} + q^{9} + O(q^{10})$$ $$12 q - 3 q^{3} - 4 q^{7} + q^{9} + 6 q^{13} - 21 q^{15} + 16 q^{19} + 8 q^{25} - 30 q^{33} + 18 q^{39} + 24 q^{43} - 34 q^{45} + 36 q^{49} - 9 q^{51} - 4 q^{55} - 15 q^{57} + 2 q^{61} + 2 q^{63} - 60 q^{67} - 42 q^{73} + 12 q^{79} - 11 q^{81} - 34 q^{85} + 18 q^{87} + 54 q^{91} + 30 q^{93} - 18 q^{97} + 26 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(228, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.2.p.a $2$ $1.821$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-3$$ $$0$$ $$-10$$ $$q+(-1-\zeta_{6})q^{3}-5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots$$
228.2.p.b $2$ $1.821$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$2$$ $$q+(1+\zeta_{6})q^{3}+q^{7}+3\zeta_{6}q^{9}+(2-\zeta_{6})q^{13}+\cdots$$
228.2.p.c $4$ $1.821$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-2$$ $$9$$ $$2$$ $$q+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$$
228.2.p.d $4$ $1.821$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-1$$ $$-9$$ $$2$$ $$q-\beta _{1}q^{3}+(-3+2\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(228, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(228, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$