# Properties

 Label 1764.2.j Level $1764$ Weight $2$ Character orbit 1764.j Rep. character $\chi_{1764}(589,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $82$ Newform subspaces $9$ Sturm bound $672$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$9$$ Sturm bound: $$672$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1764, [\chi])$$.

Total New Old
Modular forms 720 82 638
Cusp forms 624 82 542
Eisenstein series 96 0 96

## Trace form

 $$82q + q^{5} + 6q^{9} + O(q^{10})$$ $$82q + q^{5} + 6q^{9} + q^{11} - q^{13} - 17q^{15} - 16q^{17} - 4q^{19} + q^{23} - 44q^{25} - 15q^{29} - q^{31} + q^{33} + 8q^{37} + 17q^{39} - 3q^{41} + 5q^{43} + q^{45} - 3q^{47} + 20q^{51} + 28q^{53} - 6q^{55} + 42q^{57} + 25q^{59} - 13q^{61} + 13q^{65} - 7q^{67} - 23q^{69} + 44q^{71} + 8q^{73} - 34q^{75} + 11q^{79} + 14q^{81} - 7q^{83} - 6q^{85} + 77q^{87} - 48q^{89} - 29q^{93} - 13q^{97} - 17q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1764, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1764.2.j.a $$2$$ $$14.086$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$2$$ $$0$$ $$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots$$
1764.2.j.b $$2$$ $$14.086$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+(-3+\cdots)q^{11}+\cdots$$
1764.2.j.c $$2$$ $$14.086$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-2$$ $$0$$ $$q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$$
1764.2.j.d $$6$$ $$14.086$$ 6.0.309123.1 None $$0$$ $$-2$$ $$-3$$ $$0$$ $$q+(-1+\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
1764.2.j.e $$6$$ $$14.086$$ 6.0.309123.1 None $$0$$ $$2$$ $$1$$ $$0$$ $$q+(1-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
1764.2.j.f $$12$$ $$14.086$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{8}+\beta _{11})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$$
1764.2.j.g $$14$$ $$14.086$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-3$$ $$-2$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{1}-\beta _{2}+\beta _{11}+\cdots)q^{9}+\cdots$$
1764.2.j.h $$14$$ $$14.086$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$3$$ $$2$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{5}q^{5}+(-\beta _{1}-\beta _{2}+\beta _{11}+\cdots)q^{9}+\cdots$$
1764.2.j.i $$24$$ $$14.086$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1764, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(882, [\chi])$$$$^{\oplus 2}$$