# Properties

 Label 1764.3.c Level $1764$ Weight $3$ Character orbit 1764.c Rep. character $\chi_{1764}(197,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $8$ Sturm bound $1008$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1764.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$1008$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1764, [\chi])$$.

Total New Old
Modular forms 720 28 692
Cusp forms 624 28 596
Eisenstein series 96 0 96

## Trace form

 $$28 q + O(q^{10})$$ $$28 q + 8 q^{13} + 40 q^{19} - 228 q^{25} - 40 q^{31} + 4 q^{37} + 172 q^{43} + 104 q^{55} + 272 q^{61} + 60 q^{67} - 144 q^{73} - 596 q^{79} + 160 q^{85} - 96 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1764, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1764.3.c.a $$2$$ $$48.066$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}-5\beta q^{11}-23q^{13}+4\beta q^{17}+\cdots$$
1764.3.c.b $$2$$ $$48.066$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4\beta q^{5}+\beta q^{11}-2^{4}q^{13}-12\beta q^{17}+\cdots$$
1764.3.c.c $$2$$ $$48.066$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4\beta q^{5}-\beta q^{11}+2^{4}q^{13}-12\beta q^{17}+\cdots$$
1764.3.c.d $$2$$ $$48.066$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}+5\beta q^{11}+23q^{13}+4\beta q^{17}+\cdots$$
1764.3.c.e $$4$$ $$48.066$$ $$\Q(\sqrt{-2}, \sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{3})q^{11}+(-14+\cdots)q^{13}+\cdots$$
1764.3.c.f $$4$$ $$48.066$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{11}+(2-2\beta _{3})q^{13}+\cdots$$
1764.3.c.g $$4$$ $$48.066$$ $$\Q(\sqrt{-2}, \sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{3})q^{11}+\cdots$$
1764.3.c.h $$8$$ $$48.066$$ 8.0.$$\cdots$$.12 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+\beta _{5}q^{11}+3\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1764, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(882, [\chi])$$$$^{\oplus 2}$$