Properties

 Label 576.3.q Level $576$ Weight $3$ Character orbit 576.q Rep. character $\chi_{576}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $92$ Newform subspaces $12$ Sturm bound $288$ Trace bound $9$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 576.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$12$$ Sturm bound: $$288$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(576, [\chi])$$.

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

 $$92 q + 6 q^{5} - 4 q^{9} + O(q^{10})$$ $$92 q + 6 q^{5} - 4 q^{9} + 2 q^{13} - 14 q^{21} + 188 q^{25} + 6 q^{29} - 54 q^{33} + 8 q^{37} + 138 q^{41} + 6 q^{45} - 240 q^{49} - 120 q^{57} + 2 q^{61} - 6 q^{65} + 262 q^{69} - 8 q^{73} + 6 q^{77} + 140 q^{81} - 48 q^{85} + 706 q^{93} - 2 q^{97} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(576, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.q.a $2$ $15.695$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-6$$ $$2$$ $$q+(-3+3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots$$
576.3.q.b $2$ $15.695$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-6$$ $$-2$$ $$q+(3-3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
576.3.q.c $4$ $15.695$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-12$$ $$-6$$ $$6$$ $$q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$$
576.3.q.d $4$ $15.695$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-3$$ $$-9$$ $$-1$$ $$q+(-1+\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$$
576.3.q.e $4$ $15.695$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$18$$ $$-2$$ $$q+(-1+2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots$$
576.3.q.f $4$ $15.695$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$18$$ $$2$$ $$q+(1-2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots$$
576.3.q.g $4$ $15.695$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$3$$ $$-9$$ $$1$$ $$q+(1-\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots$$
576.3.q.h $4$ $15.695$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$12$$ $$-6$$ $$-6$$ $$q+3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
576.3.q.i $8$ $15.695$ 8.0.$$\cdots$$.9 None $$0$$ $$-10$$ $$6$$ $$6$$ $$q+(-1+\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$$
576.3.q.j $8$ $15.695$ 8.0.$$\cdots$$.9 None $$0$$ $$10$$ $$6$$ $$-6$$ $$q+(1-\beta _{2}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$$
576.3.q.k $24$ $15.695$ None $$0$$ $$0$$ $$0$$ $$0$$
576.3.q.l $24$ $15.695$ None $$0$$ $$0$$ $$0$$ $$0$$

Decomposition of $$S_{3}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$