# Properties

 Label 176.2.e Level $176$ Weight $2$ Character orbit 176.e Rep. character $\chi_{176}(175,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $48$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 176.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$44$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(176, [\chi])$$.

Total New Old
Modular forms 30 6 24
Cusp forms 18 6 12
Eisenstein series 12 0 12

## Trace form

 $$6 q - 18 q^{9} + O(q^{10})$$ $$6 q - 18 q^{9} + 30 q^{25} - 12 q^{45} - 42 q^{49} + 36 q^{53} - 60 q^{69} + 54 q^{81} + 84 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(176, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.2.e.a $2$ $1.405$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta q^{3}+3q^{5}-8q^{9}+\beta q^{11}-3\beta q^{15}+\cdots$$
176.2.e.b $4$ $1.405$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(176, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(176, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 2}$$