# Properties

 Label 115.2.e Level $115$ Weight $2$ Character orbit 115.e Rep. character $\chi_{115}(22,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 115.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(115, [\chi])$$.

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

## Trace form

 $$20q - 4q^{2} - 8q^{3} - 8q^{6} + 4q^{8} + O(q^{10})$$ $$20q - 4q^{2} - 8q^{3} - 8q^{6} + 4q^{8} - 16q^{12} + 4q^{13} + 8q^{16} + 8q^{18} - 12q^{25} - 16q^{26} + 4q^{27} - 4q^{31} + 24q^{32} - 8q^{35} - 32q^{36} - 36q^{41} + 32q^{46} - 8q^{47} + 4q^{48} + 60q^{50} + 40q^{52} - 12q^{55} + 36q^{58} - 60q^{62} - 76q^{70} + 44q^{71} + 72q^{72} - 56q^{73} + 28q^{75} - 12q^{77} - 44q^{78} + 92q^{81} + 28q^{82} - 4q^{85} + 24q^{87} - 72q^{92} - 8q^{93} + 64q^{95} - 104q^{96} - 60q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(115, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
115.2.e.a $$20$$ $$0.918$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$-8$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots$$