# Properties

 Label 1776.1.bq Level $1776$ Weight $1$ Character orbit 1776.bq Rep. character $\chi_{1776}(545,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $304$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1776 = 2^{4} \cdot 3 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1776.bq (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

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

## 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.bq.a $2$ $0.886$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+(-1+\cdots)q^{13}+\cdots$$

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

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