# Properties

 Label 756.2.l Level $756$ Weight $2$ Character orbit 756.l Rep. character $\chi_{756}(289,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $2$ Sturm bound $288$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$756 = 2^{2} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 756.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(756, [\chi])$$.

Total New Old
Modular forms 324 16 308
Cusp forms 252 16 236
Eisenstein series 72 0 72

## Trace form

 $$16q - 8q^{5} + q^{7} + O(q^{10})$$ $$16q - 8q^{5} + q^{7} - 4q^{11} - q^{13} + 5q^{17} + 2q^{19} + 14q^{23} + 16q^{25} - 2q^{29} + 2q^{31} + 11q^{35} - q^{37} + 24q^{41} + 2q^{43} + 6q^{47} - 11q^{49} + 18q^{53} - 12q^{55} + 7q^{59} - 13q^{61} - 9q^{65} - 7q^{67} + 14q^{71} + 14q^{73} - 35q^{77} - q^{79} + 26q^{83} - 6q^{85} + 21q^{89} + 5q^{91} + 38q^{95} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(756, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
756.2.l.a $$2$$ $$6.037$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$4$$ $$q-2q^{5}+(3-2\zeta_{6})q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots$$
756.2.l.b $$14$$ $$6.037$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$-3$$ $$q+(\beta _{3}-\beta _{7})q^{5}-\beta _{5}q^{7}+(\beta _{9}-\beta _{13})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(756, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(756, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$