# Properties

 Label 2760.1.bv Level $2760$ Weight $1$ Character orbit 2760.bv Rep. character $\chi_{2760}(137,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $8$ Newform subspaces $2$ Sturm bound $576$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2760.bv (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$345$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2760, [\chi])$$.

Total New Old
Modular forms 40 8 32
Cusp forms 8 8 0
Eisenstein series 32 0 32

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 0 0 8 0

## Trace form

 $$8 q + 4 q^{3} + O(q^{10})$$ $$8 q + 4 q^{3} + 8 q^{13} + 4 q^{27} - 8 q^{31} - 4 q^{75} + 8 q^{81} + 8 q^{85} - 4 q^{87} - 4 q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2760, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2760.1.bv.a $4$ $1.377$ $$\Q(\zeta_{8})$$ $S_{4}$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$
2760.1.bv.b $4$ $1.377$ $$\Q(\zeta_{8})$$ $S_{4}$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots$$