# Properties

 Label 342.2.s Level $342$ Weight $2$ Character orbit 342.s Rep. character $\chi_{342}(107,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $2$ Sturm bound $120$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$342 = 2 \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 342.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(342, [\chi])$$.

Total New Old
Modular forms 136 8 128
Cusp forms 104 8 96
Eisenstein series 32 0 32

## Trace form

 $$8q - 4q^{4} - 8q^{7} + O(q^{10})$$ $$8q - 4q^{4} - 8q^{7} + 12q^{13} - 4q^{16} + 32q^{19} - 24q^{22} - 12q^{25} + 4q^{28} - 24q^{34} + 4q^{43} - 12q^{52} - 16q^{55} + 4q^{61} + 8q^{64} - 12q^{67} + 24q^{70} + 28q^{73} - 4q^{76} + 36q^{79} + 8q^{85} + 60q^{91} - 72q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(342, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
342.2.s.a $$4$$ $$2.731$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$
342.2.s.b $$4$$ $$2.731$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(342, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(342, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 2}$$