# Properties

 Label 28.2.e Level $28$ Weight $2$ Character orbit 28.e Rep. character $\chi_{28}(9,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $2$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 28.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(28, [\chi])$$.

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

## Trace form

 $$2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + O(q^{10})$$ $$2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} + 4 q^{13} + 6 q^{15} - 3 q^{17} + q^{19} - q^{21} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} + 7 q^{31} + 3 q^{33} + 15 q^{35} + q^{37} - 2 q^{39} + 12 q^{41} - 8 q^{43} + 6 q^{45} + 9 q^{47} + 2 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} - 2 q^{57} - 9 q^{59} + q^{61} - 10 q^{63} - 6 q^{65} + 7 q^{67} + 6 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 13 q^{79} - q^{81} + 24 q^{83} + 18 q^{85} + 6 q^{87} - 15 q^{89} - 8 q^{91} + 7 q^{93} + 3 q^{95} - 20 q^{97} + 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(28, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.2.e.a $2$ $0.224$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$-4$$ $$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$