# Properties

 Label 1776.1.bw Level $1776$ Weight $1$ Character orbit 1776.bw Rep. character $\chi_{1776}(1025,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $304$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1776 = 2^{4} \cdot 3 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1776.bw (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$304$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1776, [\chi])$$.

Total New Old
Modular forms 36 6 30
Cusp forms 12 2 10
Eisenstein series 24 4 20

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q + q^{3} - q^{7} - q^{9} + O(q^{10})$$ $$2q + q^{3} - q^{7} - q^{9} + q^{13} + 2q^{19} + q^{21} - q^{25} - 2q^{27} + 2q^{31} + 2q^{37} - q^{39} + 2q^{43} - 2q^{57} - 2q^{61} + 2q^{63} - q^{67} - 2q^{73} - 2q^{75} - q^{79} - q^{81} + q^{91} + q^{93} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1776, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1776.1.bw.a $$2$$ $$0.886$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+\zeta_{6}q^{3}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1776, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1776, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(111, [\chi])$$$$^{\oplus 5}$$