Properties

 Label 1764.2.b Level $1764$ Weight $2$ Character orbit 1764.b Rep. character $\chi_{1764}(1567,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $14$ Sturm bound $672$ Trace bound $50$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$14$$ Sturm bound: $$672$$ Trace bound: $$50$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$19$$, $$29$$, $$53$$

Dimensions

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

Total New Old
Modular forms 368 104 264
Cusp forms 304 96 208
Eisenstein series 64 8 56

Trace form

 $$96 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + O(q^{10})$$ $$96 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{16} - 20 q^{22} - 68 q^{25} - 16 q^{29} - 4 q^{32} - 4 q^{37} + 24 q^{44} + 28 q^{46} + 56 q^{50} + 20 q^{53} + 64 q^{58} + 52 q^{64} + 8 q^{65} + 12 q^{85} - 36 q^{86} - 64 q^{88} - 8 q^{92} + O(q^{100})$$

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.b.a $$4$$ $$14.086$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$$
1764.2.b.b $$4$$ $$14.086$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots$$
1764.2.b.c $$4$$ $$14.086$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$$
1764.2.b.d $$4$$ $$14.086$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$$
1764.2.b.e $$4$$ $$14.086$$ 4.0.2048.2 $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots$$
1764.2.b.f $$4$$ $$14.086$$ 4.0.2048.2 $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots$$
1764.2.b.g $$4$$ $$14.086$$ 4.0.2048.2 $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots$$
1764.2.b.h $$4$$ $$14.086$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots$$
1764.2.b.i $$8$$ $$14.086$$ 8.0.562828176.1 None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots$$
1764.2.b.j $$8$$ $$14.086$$ 8.0.562828176.1 None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots$$
1764.2.b.k $$8$$ $$14.086$$ 8.0.$$\cdots$$.10 None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots$$
1764.2.b.l $$12$$ $$14.086$$ 12.0.$$\cdots$$.1 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$$
1764.2.b.m $$12$$ $$14.086$$ 12.0.$$\cdots$$.1 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$$
1764.2.b.n $$16$$ $$14.086$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 2}$$