Properties

 Label 65.2.b Level $65$ Weight $2$ Character orbit 65.b Rep. character $\chi_{65}(14,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $14$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$65 = 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 65.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$14$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(65, [\chi])$$.

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

 $$6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + O(q^{10})$$ $$6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 16 q^{15} + 10 q^{16} - 20 q^{20} - 4 q^{21} + 16 q^{24} + 2 q^{25} - 6 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} + 20 q^{34} + 8 q^{35} - 22 q^{36} + 8 q^{39} - 34 q^{40} - 8 q^{41} + 40 q^{44} - 4 q^{45} + 32 q^{46} + 18 q^{49} + 16 q^{50} + 24 q^{51} - 68 q^{54} - 16 q^{55} + 40 q^{56} + 16 q^{59} - 12 q^{60} + 12 q^{61} - 66 q^{64} - 2 q^{65} - 16 q^{66} - 24 q^{69} - 20 q^{70} - 24 q^{71} + 4 q^{74} + 16 q^{75} - 20 q^{76} + 32 q^{79} + 48 q^{80} + 46 q^{81} + 12 q^{84} - 12 q^{85} - 32 q^{86} - 20 q^{89} + 70 q^{90} - 4 q^{91} - 32 q^{94} + 16 q^{95} - 36 q^{96} + 16 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(65, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
65.2.b.a $6$ $0.519$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$$