# Properties

 Label 228.2.i Level $228$ Weight $2$ Character orbit 228.i Rep. character $\chi_{228}(49,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $2$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$80$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 92 8 84
Cusp forms 68 8 60
Eisenstein series 24 0 24

## Trace form

 $$8 q - 2 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10})$$ $$8 q - 2 q^{5} + 4 q^{7} - 4 q^{9} + 12 q^{11} + 2 q^{15} - 4 q^{17} + 4 q^{19} + 6 q^{21} + 18 q^{23} - 8 q^{25} - 4 q^{29} - 20 q^{31} + 6 q^{33} - 6 q^{35} - 24 q^{37} - 8 q^{39} - 8 q^{41} - 14 q^{43} + 4 q^{45} - 12 q^{47} + 16 q^{49} + 4 q^{51} + 2 q^{53} + 20 q^{55} - 14 q^{57} - 10 q^{59} + 4 q^{61} - 2 q^{63} - 52 q^{65} + 2 q^{67} - 12 q^{69} + 8 q^{71} + 16 q^{73} - 8 q^{75} + 20 q^{77} - 22 q^{79} - 4 q^{81} - 8 q^{83} - 8 q^{87} - 10 q^{89} + 22 q^{91} + 18 q^{93} + 62 q^{95} + 8 q^{97} - 6 q^{99} + O(q^{100})$$

## 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.i.a $4$ $1.821$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$$
228.2.i.b $4$ $1.821$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$2$$ $$-2$$ $$8$$ $$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(228, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$