# Properties

 Label 342.3.r Level $342$ Weight $3$ Character orbit 342.r Rep. character $\chi_{342}(125,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $4$ Sturm bound $180$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$342 = 2 \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 342.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$180$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(342, [\chi])$$.

Total New Old
Modular forms 256 32 224
Cusp forms 224 32 192
Eisenstein series 32 0 32

## Trace form

 $$32 q + 32 q^{4} + O(q^{10})$$ $$32 q + 32 q^{4} - 16 q^{13} - 64 q^{16} + 56 q^{19} - 16 q^{22} + 248 q^{25} - 112 q^{31} - 16 q^{34} + 240 q^{37} - 136 q^{43} + 320 q^{46} + 672 q^{49} + 32 q^{52} - 216 q^{55} - 192 q^{58} - 8 q^{61} - 256 q^{64} - 376 q^{67} - 144 q^{70} + 24 q^{73} - 64 q^{76} + 120 q^{79} + 176 q^{82} - 816 q^{85} - 64 q^{88} - 8 q^{91} - 64 q^{94} + 496 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(342, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.3.r.a $4$ $9.319$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-52$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+6\beta _{1}q^{5}-13q^{7}+\cdots$$
342.3.r.b $4$ $9.319$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-28$$ $$q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-7q^{7}+\cdots$$
342.3.r.c $12$ $9.319$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$20$$ $$q+\beta _{5}q^{2}+(2+2\beta _{1})q^{4}+(-\beta _{3}-2\beta _{5}+\cdots)q^{5}+\cdots$$
342.3.r.d $12$ $9.319$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$60$$ $$q-\beta _{5}q^{2}-2\beta _{2}q^{4}+(-\beta _{5}-\beta _{11})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(342, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(342, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 2}$$