# Properties

 Label 28.4.e Level $28$ Weight $4$ Character orbit 28.e Rep. character $\chi_{28}(9,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ 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: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(28, [\chi])$$.

Total New Old
Modular forms 30 4 26
Cusp forms 18 4 14
Eisenstein series 12 0 12

## Trace form

 $$4q + 14q^{5} + 24q^{7} - 20q^{9} + O(q^{10})$$ $$4q + 14q^{5} + 24q^{7} - 20q^{9} - 32q^{11} - 56q^{13} - 296q^{15} + 154q^{17} + 224q^{19} + 370q^{21} - 68q^{23} - 144q^{25} - 472q^{29} + 196q^{31} + 518q^{33} + 400q^{35} - 346q^{37} - 296q^{39} - 840q^{41} - 688q^{43} + 140q^{45} - 84q^{47} + 100q^{49} + 296q^{51} + 438q^{53} + 1624q^{55} + 444q^{57} + 56q^{59} - 98q^{61} - 360q^{63} + 396q^{65} - 336q^{67} - 1036q^{69} + 1792q^{71} - 966q^{73} - 2072q^{75} - 2398q^{77} + 52q^{79} + 1798q^{81} + 784q^{83} + 3340q^{85} - 2072q^{87} - 294q^{89} - 1520q^{91} - 518q^{93} - 1124q^{95} - 840q^{97} + 640q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(28, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
28.4.e.a $$4$$ $$1.652$$ $$\Q(\sqrt{-3}, \sqrt{37})$$ None $$0$$ $$0$$ $$14$$ $$24$$ $$q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(28, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(28, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 2}$$