# Properties

 Label 176.2.m Level $176$ Weight $2$ Character orbit 176.m Rep. character $\chi_{176}(49,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $20$ Newform subspaces $4$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 176.m (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$3$$ 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 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

## Trace form

 $$20 q + 3 q^{3} - 3 q^{5} + q^{7} - 10 q^{9} + O(q^{10})$$ $$20 q + 3 q^{3} - 3 q^{5} + q^{7} - 10 q^{9} + 2 q^{11} - 3 q^{13} + 3 q^{15} - 7 q^{17} + 9 q^{19} - 2 q^{21} + 16 q^{23} - 12 q^{25} + 3 q^{27} + 5 q^{29} + 3 q^{31} + 5 q^{33} - 13 q^{35} - 15 q^{37} - 47 q^{39} + 13 q^{41} - 36 q^{43} + 8 q^{45} - 9 q^{47} + 2 q^{49} - 27 q^{51} - 23 q^{53} - 21 q^{55} + 13 q^{57} + 7 q^{59} - 11 q^{61} - 12 q^{63} - 6 q^{65} + 12 q^{67} - 28 q^{69} + 25 q^{71} - 3 q^{73} + 17 q^{75} + 15 q^{77} + 35 q^{79} + 28 q^{81} + 63 q^{83} + 31 q^{85} + 110 q^{87} - 4 q^{89} + 17 q^{91} + 11 q^{93} + 7 q^{95} + 19 q^{97} + 46 q^{99} + O(q^{100})$$

## 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.m.a $4$ $1.405$ $$\Q(\zeta_{10})$$ None $$0$$ $$-3$$ $$3$$ $$3$$ $$q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$$
176.2.m.b $4$ $1.405$ $$\Q(\zeta_{10})$$ None $$0$$ $$1$$ $$3$$ $$7$$ $$q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$$
176.2.m.c $4$ $1.405$ $$\Q(\zeta_{10})$$ None $$0$$ $$4$$ $$-6$$ $$-2$$ $$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$$
176.2.m.d $8$ $1.405$ 8.0.682515625.5 None $$0$$ $$1$$ $$-3$$ $$-7$$ $$q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(176, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 2}$$