# Properties

 Label 182.2.w Level $182$ Weight $2$ Character orbit 182.w Rep. character $\chi_{182}(19,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $40$ Newform subspaces $1$ Sturm bound $56$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$182 = 2 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 182.w (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(182, [\chi])$$.

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

## Trace form

 $$40q - 8q^{7} - 48q^{9} + O(q^{10})$$ $$40q - 8q^{7} - 48q^{9} - 12q^{11} - 4q^{12} - 4q^{14} - 16q^{15} + 20q^{16} - 8q^{18} + 16q^{19} + 24q^{21} + 4q^{22} + 8q^{28} + 4q^{29} + 16q^{31} - 24q^{33} - 20q^{35} - 24q^{36} + 40q^{37} + 12q^{39} + 24q^{41} + 24q^{42} - 72q^{43} + 12q^{46} + 36q^{47} - 28q^{49} + 24q^{51} - 16q^{52} - 4q^{53} + 12q^{55} - 12q^{56} - 12q^{57} - 32q^{58} + 16q^{60} + 36q^{62} + 16q^{63} - 52q^{65} - 16q^{67} - 12q^{68} - 84q^{69} - 88q^{70} + 28q^{71} - 16q^{72} - 76q^{73} - 20q^{74} + 28q^{75} - 32q^{76} + 8q^{78} - 16q^{79} - 8q^{81} + 96q^{82} + 108q^{83} + 32q^{84} + 56q^{85} - 32q^{86} + 24q^{87} + 48q^{89} + 44q^{91} + 32q^{92} + 48q^{93} + 24q^{95} - 88q^{97} - 8q^{98} + 28q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(182, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
182.2.w.a $$40$$ $$1.453$$ None $$0$$ $$0$$ $$0$$ $$-8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(182, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(182, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$