# Properties

 Label 95.3.d Level $95$ Weight $3$ Character orbit 95.d Rep. character $\chi_{95}(94,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $4$ Sturm bound $30$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$30$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(95, [\chi])$$.

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

## Trace form

 $$18q + 32q^{4} - q^{5} - 8q^{6} + 38q^{9} + O(q^{10})$$ $$18q + 32q^{4} - q^{5} - 8q^{6} + 38q^{9} - 22q^{11} + 72q^{16} + 10q^{19} + 60q^{20} - 256q^{24} + 55q^{25} - 176q^{26} - 264q^{30} + 41q^{35} + 32q^{36} + 184q^{39} - 144q^{44} + 33q^{45} + 164q^{49} - 13q^{55} - 30q^{61} + 392q^{64} + 168q^{66} + 384q^{74} - 24q^{76} + 256q^{80} + 594q^{81} + 195q^{85} - 597q^{95} - 1312q^{96} - 1178q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
95.3.d.a $$2$$ $$2.589$$ $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-9$$ $$0$$ $$q-4q^{4}+(-4-\beta )q^{5}+(-3+6\beta )q^{7}+\cdots$$
95.3.d.b $$4$$ $$2.589$$ 4.4.462080.1 $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$-20$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(4+\beta _{3})q^{4}+\cdots$$
95.3.d.c $$4$$ $$2.589$$ 4.4.7600.1 $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$20$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(4+3\beta _{3})q^{4}+\cdots$$
95.3.d.d $$8$$ $$2.589$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+2\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$$