Properties

 Label 27.3.b Level $27$ Weight $3$ Character orbit 27.b Rep. character $\chi_{27}(26,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $9$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$27 = 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 27.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$9$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(27, [\chi])$$.

Total New Old
Modular forms 9 3 6
Cusp forms 3 3 0
Eisenstein series 6 0 6

Trace form

 $$3 q - 6 q^{4} - 3 q^{7} + O(q^{10})$$ $$3 q - 6 q^{4} - 3 q^{7} + 18 q^{10} - 21 q^{13} - 6 q^{16} - 21 q^{19} + 90 q^{22} + 57 q^{25} - 102 q^{28} - 48 q^{31} - 108 q^{34} + 87 q^{37} - 18 q^{40} + 78 q^{43} + 72 q^{46} + 72 q^{49} + 96 q^{52} - 90 q^{55} - 180 q^{58} - 273 q^{61} + 246 q^{64} - 129 q^{67} + 90 q^{70} + 33 q^{73} + 204 q^{76} + 159 q^{79} - 360 q^{82} + 108 q^{85} - 90 q^{88} - 87 q^{91} + 36 q^{94} - 3 q^{97} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(27, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.3.b.a $1$ $0.736$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-13$$ $$q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots$$
27.3.b.b $2$ $0.736$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$10$$ $$q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots$$