Properties

 Label 2736.2.dc Level $2736$ Weight $2$ Character orbit 2736.dc Rep. character $\chi_{2736}(449,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $6$ Sturm bound $960$ Trace bound $17$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.dc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$960$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2736, [\chi])$$.

Total New Old
Modular forms 1008 80 928
Cusp forms 912 80 832
Eisenstein series 96 0 96

Trace form

 $$80q + 8q^{7} + O(q^{10})$$ $$80q + 8q^{7} - 16q^{19} + 40q^{25} + 4q^{43} + 64q^{49} - 24q^{55} - 32q^{61} - 60q^{67} + 8q^{73} - 84q^{79} - 12q^{91} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2736.2.dc.a $$4$$ $$21.847$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{5}+(1-2\beta _{1}+\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots$$
2736.2.dc.b $$4$$ $$21.847$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{5}+(1+2\beta _{1}-\beta _{3})q^{7}+(2-4\beta _{2}+\cdots)q^{11}+\cdots$$
2736.2.dc.c $$16$$ $$21.847$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{10}q^{5}-\beta _{14}q^{7}-\beta _{7}q^{11}+(-2+\cdots)q^{13}+\cdots$$
2736.2.dc.d $$16$$ $$21.847$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{10})q^{5}+(-\beta _{7}-\beta _{8})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$$
2736.2.dc.e $$20$$ $$21.847$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(\beta _{6}+\beta _{18}+\cdots)q^{11}+\cdots$$
2736.2.dc.f $$20$$ $$21.847$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(-\beta _{6}+\cdots)q^{11}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(912, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1368, [\chi])$$$$^{\oplus 2}$$