Properties

 Label 176.2.q Level $176$ Weight $2$ Character orbit 176.q Rep. character $\chi_{176}(63,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $24$ 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.q (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$44$$ Character field: $$\Q(\zeta_{10})$$ 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 120 24 96
Cusp forms 72 24 48
Eisenstein series 48 0 48

Trace form

 $$24 q + 18 q^{9} + O(q^{10})$$ $$24 q + 18 q^{9} - 30 q^{25} - 30 q^{33} - 60 q^{41} - 48 q^{45} - 18 q^{49} - 36 q^{53} - 30 q^{57} + 60 q^{69} + 60 q^{73} + 60 q^{77} + 36 q^{81} + 120 q^{85} + 60 q^{89} + 36 q^{93} + 90 q^{97} + O(q^{100})$$

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.q.a $8$ $1.405$ 8.0.484000000.6 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
176.2.q.b $16$ $1.405$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$6$$ $$0$$ $$q+(\beta _{2}+\beta _{4}-\beta _{6}-\beta _{9}+\beta _{11})q^{3}+(1+\cdots)q^{5}+\cdots$$

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

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