# Properties

 Label 34.2.c Level $34$ Weight $2$ Character orbit 34.c Rep. character $\chi_{34}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $2$ Sturm bound $9$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$34 = 2 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 34.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$9$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(34, [\chi])$$.

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

## Trace form

 $$4 q - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + O(q^{10})$$ $$4 q - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{13} + 4 q^{14} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 8 q^{21} - 10 q^{22} + 8 q^{23} + 2 q^{24} - 8 q^{27} + 4 q^{28} - 10 q^{29} - 8 q^{30} + 4 q^{31} - 4 q^{33} - 6 q^{34} - 16 q^{35} + 6 q^{37} - 16 q^{38} + 12 q^{39} - 6 q^{40} + 4 q^{41} + 6 q^{44} - 2 q^{45} + 8 q^{46} + 32 q^{47} - 2 q^{48} + 12 q^{50} - 6 q^{51} + 4 q^{52} + 8 q^{54} + 24 q^{55} - 4 q^{56} - 8 q^{57} + 2 q^{58} - 26 q^{61} + 20 q^{62} + 4 q^{63} - 4 q^{64} - 32 q^{65} - 28 q^{67} - 6 q^{68} - 16 q^{71} - 4 q^{72} + 8 q^{73} - 6 q^{74} + 6 q^{75} + 12 q^{78} + 2 q^{80} - 8 q^{81} - 8 q^{84} + 22 q^{85} - 4 q^{86} + 10 q^{88} - 10 q^{90} + 24 q^{91} - 8 q^{92} + 24 q^{95} - 2 q^{96} - 4 q^{97} - 16 q^{98} + 22 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(34, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
34.2.c.a $2$ $0.271$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$4$$ $$-4$$ $$q-iq^{2}+(-1-i)q^{3}-q^{4}+(2+2i)q^{5}+\cdots$$
34.2.c.b $2$ $0.271$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$$