# Properties

 Label 156.2.u Level $156$ Weight $2$ Character orbit 156.u Rep. character $\chi_{156}(41,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $20$ Newform subspaces $2$ Sturm bound $56$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$156 = 2^{2} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 156.u (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(156, [\chi])$$.

Total New Old
Modular forms 136 20 116
Cusp forms 88 20 68
Eisenstein series 48 0 48

## Trace form

 $$20q - 2q^{7} + O(q^{10})$$ $$20q - 2q^{7} + 12q^{15} + 10q^{19} - 12q^{21} - 36q^{27} - 10q^{31} - 30q^{33} + 2q^{37} - 42q^{43} - 30q^{45} - 18q^{49} + 18q^{57} + 30q^{63} - 32q^{67} + 78q^{69} + 10q^{73} + 90q^{75} + 96q^{79} - 12q^{81} + 96q^{85} + 22q^{91} + 48q^{93} + 38q^{97} - 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(156, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
156.2.u.a $$4$$ $$1.246$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}-3\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$
156.2.u.b $$16$$ $$1.246$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{9}-\beta _{13}-\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(156, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(156, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$