Properties

 Label 90.3.b Level $90$ Weight $3$ Character orbit 90.b Rep. character $\chi_{90}(89,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $54$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 90.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$54$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(90, [\chi])$$.

Total New Old
Modular forms 44 4 40
Cusp forms 28 4 24
Eisenstein series 16 0 16

Trace form

 $$4 q + 8 q^{4} + O(q^{10})$$ $$4 q + 8 q^{4} + 20 q^{10} + 16 q^{16} - 96 q^{19} + 16 q^{31} + 8 q^{34} + 40 q^{40} - 224 q^{46} + 132 q^{49} - 160 q^{55} + 440 q^{61} + 32 q^{64} + 80 q^{70} - 192 q^{76} + 144 q^{79} + 20 q^{85} - 288 q^{91} + 160 q^{94} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(90, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
90.3.b.a $4$ $2.452$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}-4\zeta_{8}^{2}q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(90, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(90, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$