# Properties

 Label 2736.3.m Level $2736$ Weight $3$ Character orbit 2736.m Rep. character $\chi_{2736}(1711,\cdot)$ Character field $\Q$ Dimension $90$ Newform subspaces $7$ Sturm bound $1440$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2736.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$1440$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2736, [\chi])$$.

Total New Old
Modular forms 984 90 894
Cusp forms 936 90 846
Eisenstein series 48 0 48

## Trace form

 $$90q + 12q^{5} + O(q^{10})$$ $$90q + 12q^{5} - 36q^{13} - 12q^{17} + 534q^{25} + 204q^{29} + 12q^{37} - 60q^{41} - 390q^{49} + 60q^{53} + 60q^{61} + 72q^{65} - 300q^{73} + 312q^{77} - 48q^{85} - 204q^{89} - 60q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2736.3.m.a $$6$$ $$74.551$$ 6.0.210056875.1 None $$0$$ $$0$$ $$-14$$ $$0$$ $$q+(-2+\beta _{2})q^{5}+(\beta _{1}+2\beta _{4}-\beta _{5})q^{7}+\cdots$$
2736.3.m.b $$12$$ $$74.551$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+\beta _{8}q^{7}-\beta _{6}q^{11}+\beta _{1}q^{13}+\cdots$$
2736.3.m.c $$12$$ $$74.551$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-\beta _{6}+\beta _{9}+\cdots)q^{11}+\cdots$$
2736.3.m.d $$12$$ $$74.551$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{2}q^{5}-\beta _{7}q^{7}+(-\beta _{6}-\beta _{7}-2\beta _{8}+\cdots)q^{11}+\cdots$$
2736.3.m.e $$12$$ $$74.551$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$10$$ $$0$$ $$q+(1+\beta _{1})q^{5}-\beta _{10}q^{7}+(\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{11}+\cdots$$
2736.3.m.f $$12$$ $$74.551$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$10$$ $$0$$ $$q+(1-\beta _{2})q^{5}-\beta _{11}q^{7}+(-\beta _{7}+\beta _{9}+\cdots)q^{11}+\cdots$$
2736.3.m.g $$24$$ $$74.551$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(912, [\chi])$$$$^{\oplus 2}$$