Properties

 Label 462.2.e Level $462$ Weight $2$ Character orbit 462.e Rep. character $\chi_{462}(307,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $192$ Trace bound $6$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$13$$

Dimensions

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

Total New Old
Modular forms 104 16 88
Cusp forms 88 16 72
Eisenstein series 16 0 16

Trace form

 $$16q - 16q^{4} - 16q^{9} + O(q^{10})$$ $$16q - 16q^{4} - 16q^{9} - 16q^{11} - 16q^{14} + 8q^{15} + 16q^{16} + 8q^{22} - 16q^{23} - 32q^{25} + 16q^{36} + 32q^{37} + 16q^{44} - 24q^{49} + 16q^{56} - 8q^{60} - 16q^{64} + 32q^{67} - 24q^{70} + 16q^{71} - 16q^{77} + 16q^{81} - 48q^{86} - 8q^{88} + 40q^{91} + 16q^{92} + 40q^{93} + 16q^{99} + O(q^{100})$$

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.e.a $$8$$ $$3.689$$ 8.0.6679465984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
462.2.e.b $$8$$ $$3.689$$ 8.0.6679465984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$