Properties

 Label 342.3.d Level $342$ Weight $3$ Character orbit 342.d Rep. character $\chi_{342}(37,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $3$ Sturm bound $180$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$342 = 2 \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 342.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$180$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

Dimensions

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

Total New Old
Modular forms 128 18 110
Cusp forms 112 18 94
Eisenstein series 16 0 16

Trace form

 $$18 q - 36 q^{4} - 2 q^{5} + 10 q^{7} + O(q^{10})$$ $$18 q - 36 q^{4} - 2 q^{5} + 10 q^{7} - 14 q^{11} + 72 q^{16} + 46 q^{17} - 10 q^{19} + 4 q^{20} + 76 q^{23} + 64 q^{25} + 48 q^{26} - 20 q^{28} - 226 q^{35} - 48 q^{38} + 114 q^{43} + 28 q^{44} + 178 q^{47} + 168 q^{49} - 194 q^{55} + 24 q^{58} - 146 q^{61} - 24 q^{62} - 144 q^{64} - 92 q^{68} + 102 q^{73} + 120 q^{74} + 20 q^{76} - 118 q^{77} - 8 q^{80} - 120 q^{82} + 124 q^{83} - 134 q^{85} - 152 q^{92} + 178 q^{95} + O(q^{100})$$

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.d.a $2$ $9.319$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$2$$ $$10$$ $$q-\beta q^{2}-2q^{4}+q^{5}+5q^{7}+2\beta q^{8}+\cdots$$
342.3.d.b $8$ $9.319$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$-4$$ $$-12$$ $$q+\beta _{2}q^{2}-2q^{4}-\beta _{5}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$$
342.3.d.c $8$ $9.319$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$12$$ $$q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(342, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 2}$$