Properties

 Label 462.2.k Level $462$ Weight $2$ Character orbit 462.k Rep. character $\chi_{462}(89,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $7$ Sturm bound $192$ Trace bound $15$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$7$$ Sturm bound: $$192$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$5$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(462, [\chi])$$.

Total New Old
Modular forms 208 56 152
Cusp forms 176 56 120
Eisenstein series 32 0 32

Trace form

 $$56q + 28q^{4} + 16q^{7} + 4q^{9} + O(q^{10})$$ $$56q + 28q^{4} + 16q^{7} + 4q^{9} - 8q^{15} - 28q^{16} + 8q^{18} - 24q^{19} + 16q^{21} - 12q^{24} - 36q^{25} + 8q^{28} + 24q^{31} + 8q^{36} - 12q^{37} - 20q^{39} + 36q^{42} + 48q^{45} + 16q^{46} - 40q^{49} + 4q^{51} - 24q^{52} - 36q^{54} + 8q^{57} + 12q^{58} - 4q^{60} - 56q^{63} - 56q^{64} + 32q^{70} - 8q^{72} + 48q^{73} - 36q^{75} - 20q^{81} + 24q^{82} - 4q^{84} + 16q^{85} - 36q^{87} - 16q^{91} - 28q^{93} - 48q^{94} - 12q^{96} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(462, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
462.2.k.a $$4$$ $$3.689$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
462.2.k.b $$4$$ $$3.689$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
462.2.k.c $$4$$ $$3.689$$ $$\Q(\zeta_{12})$$ None $$0$$ $$6$$ $$0$$ $$2$$ $$q+\zeta_{12}q^{2}+(2-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
462.2.k.d $$8$$ $$3.689$$ $$\Q(\zeta_{24})$$ None $$0$$ $$-12$$ $$0$$ $$4$$ $$q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(-1-\zeta_{24}^{2}+\cdots)q^{3}+\cdots$$
462.2.k.e $$8$$ $$3.689$$ $$\Q(\zeta_{24})$$ None $$0$$ $$4$$ $$-4$$ $$0$$ $$q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}-\zeta_{24}^{2}+\cdots)q^{3}+\cdots$$
462.2.k.f $$8$$ $$3.689$$ $$\Q(\zeta_{24})$$ None $$0$$ $$8$$ $$4$$ $$0$$ $$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$
462.2.k.g $$20$$ $$3.689$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$-6$$ $$q-\beta _{7}q^{2}-\beta _{12}q^{3}-\beta _{3}q^{4}+(2\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(462, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$