Properties

 Label 1386.2.bu Level $1386$ Weight $2$ Character orbit 1386.bu Rep. character $\chi_{1386}(701,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $96$ Newform subspaces $2$ Sturm bound $576$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.bu (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1386, [\chi])$$.

Total New Old
Modular forms 1216 96 1120
Cusp forms 1088 96 992
Eisenstein series 128 0 128

Trace form

 $$96q - 24q^{4} + O(q^{10})$$ $$96q - 24q^{4} - 24q^{16} + 8q^{22} + 48q^{25} + 80q^{31} - 32q^{34} + 32q^{37} - 80q^{46} + 24q^{49} - 80q^{52} - 64q^{55} - 32q^{58} + 80q^{61} - 24q^{64} + 96q^{67} + 16q^{70} + 80q^{73} + 80q^{79} - 32q^{82} - 40q^{85} + 8q^{88} - 16q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1386, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1386.2.bu.a $$48$$ $$11.067$$ None $$-12$$ $$0$$ $$0$$ $$0$$
1386.2.bu.b $$48$$ $$11.067$$ None $$12$$ $$0$$ $$0$$ $$0$$

Decomposition of $$S_{2}^{\mathrm{old}}(1386, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(198, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$