# Properties

 Label 28.3.h Level 28 Weight 3 Character orbit h Rep. character $$\chi_{28}(5,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 2 Newforms 1 Sturm bound 12 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 28.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q(\zeta_{6})$$ Newforms: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(28, [\chi])$$.

Total New Old
Modular forms 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

## Trace form

 $$2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} + O(q^{10})$$ $$2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} - 15q^{11} + 6q^{15} + 51q^{17} + 27q^{19} - 21q^{21} + 9q^{23} - 22q^{25} - 12q^{29} - 21q^{31} - 45q^{33} - 21q^{35} - 31q^{37} + 24q^{39} + 20q^{43} - 18q^{45} + 75q^{47} + 98q^{49} + 51q^{51} + 57q^{53} + 54q^{57} - 141q^{59} - 141q^{61} + 42q^{63} - 24q^{65} + 49q^{67} - 252q^{71} - 45q^{73} - 66q^{75} + 105q^{77} + 73q^{79} - 9q^{81} + 102q^{85} - 18q^{87} + 99q^{89} - 21q^{93} + 27q^{95} + 180q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(28, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
28.3.h.a $$2$$ $$0.763$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$3$$ $$-14$$ $$q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(28, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(28, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 2}$$