Properties

 Label 330.2.j Level $330$ Weight $2$ Character orbit 330.j Rep. character $\chi_{330}(23,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $2$ Sturm bound $144$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$330 = 2 \cdot 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 330.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$144$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(330, [\chi])$$.

Total New Old
Modular forms 160 40 120
Cusp forms 128 40 88
Eisenstein series 32 0 32

Trace form

 $$40q + 4q^{3} + 8q^{6} + O(q^{10})$$ $$40q + 4q^{3} + 8q^{6} - 4q^{12} + 16q^{13} - 20q^{15} - 40q^{16} - 16q^{18} + 24q^{25} + 4q^{27} + 24q^{30} + 32q^{31} - 4q^{33} - 8q^{36} - 8q^{37} - 16q^{40} + 24q^{42} - 16q^{45} - 48q^{46} - 4q^{48} - 32q^{51} - 16q^{52} - 24q^{55} - 16q^{58} + 12q^{60} + 16q^{61} + 48q^{63} + 40q^{67} - 16q^{70} + 16q^{72} - 16q^{73} + 12q^{75} - 32q^{76} + 16q^{78} + 48q^{82} - 104q^{87} + 16q^{90} - 104q^{93} - 8q^{96} - 88q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(330, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
330.2.j.a $$20$$ $$2.635$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}-\beta _{3}q^{3}-\beta _{14}q^{4}+(\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$$
330.2.j.b $$20$$ $$2.635$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+\beta _{1}q^{3}-\beta _{14}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(330, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(330, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$