Properties

 Label 1080.1.i Level $1080$ Weight $1$ Character orbit 1080.i Rep. character $\chi_{1080}(269,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $6$ Sturm bound $216$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1080 = 2^{3} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1080.i (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$120$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$216$$ Trace bound: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1080, [\chi])$$.

Total New Old
Modular forms 30 12 18
Cusp forms 18 12 6
Eisenstein series 12 0 12

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

Trace form

 $$12 q + 2 q^{4} + O(q^{10})$$ $$12 q + 2 q^{4} - 4 q^{10} + 6 q^{16} + 2 q^{25} + 4 q^{31} - 10 q^{34} - 2 q^{40} + 2 q^{46} - 10 q^{55} - 4 q^{64} - 6 q^{70} + 6 q^{76} - 4 q^{94} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(1080, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1080.1.i.a $1$ $0.539$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-30})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$$
1080.1.i.b $1$ $0.539$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-30})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots$$
1080.1.i.c $1$ $0.539$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-30})$$ None $$1$$ $$0$$ $$-1$$ $$0$$ $$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots$$
1080.1.i.d $1$ $0.539$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-30})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$$
1080.1.i.e $4$ $0.539$ $$\Q(\zeta_{12})$$ $D_{6}$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$
1080.1.i.f $4$ $0.539$ $$\Q(\zeta_{12})$$ $D_{6}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$

Decomposition of $$S_{1}^{\mathrm{old}}(1080, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1080, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 2}$$