Properties

 Label 2592.2.i Level $2592$ Weight $2$ Character orbit 2592.i Rep. character $\chi_{2592}(865,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $96$ Newform subspaces $34$ Sturm bound $864$ Trace bound $13$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2592 = 2^{5} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2592.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$34$$ Sturm bound: $$864$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2592, [\chi])$$.

Total New Old
Modular forms 960 96 864
Cusp forms 768 96 672
Eisenstein series 192 0 192

Trace form

 $$96 q + O(q^{10})$$ $$96 q - 48 q^{25} - 48 q^{49} - 48 q^{73} + 24 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(2592, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2592.2.i.a $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-4$$ $$0$$ $$q-4\zeta_{6}q^{5}+6\zeta_{6}q^{13}+8q^{17}+(-11+\cdots)q^{25}+\cdots$$
2592.2.i.b $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-4$$ $$q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$$
2592.2.i.c $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-3$$ $$q-2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
2592.2.i.d $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-1$$ $$q-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2592.2.i.e $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q-2\zeta_{6}q^{5}-6\zeta_{6}q^{13}-2q^{17}+(1-\zeta_{6})q^{25}+\cdots$$
2592.2.i.f $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$1$$ $$q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2592.2.i.g $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$3$$ $$q-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
2592.2.i.h $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$4$$ $$q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$$
2592.2.i.i $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-3$$ $$q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
2592.2.i.j $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2592.2.i.k $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$2$$ $$q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2592.2.i.l $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$3$$ $$q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
2592.2.i.m $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-3$$ $$q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
2592.2.i.n $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2592.2.i.o $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$2$$ $$q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2592.2.i.p $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$3$$ $$q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
2592.2.i.q $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-4$$ $$q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$$
2592.2.i.r $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-3$$ $$q+2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
2592.2.i.s $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-1$$ $$q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2592.2.i.t $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+2\zeta_{6}q^{5}-6\zeta_{6}q^{13}+2q^{17}+(1-\zeta_{6})q^{25}+\cdots$$
2592.2.i.u $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2592.2.i.v $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$3$$ $$q+2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
2592.2.i.w $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$4$$ $$q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$$
2592.2.i.x $$2$$ $$20.697$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$4$$ $$0$$ $$q+4\zeta_{6}q^{5}+6\zeta_{6}q^{13}-8q^{17}+(-11+\cdots)q^{25}+\cdots$$
2592.2.i.y $$4$$ $$20.697$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-3\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{13}+\cdots$$
2592.2.i.z $$4$$ $$20.697$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+\beta _{2}q^{11}+\cdots$$
2592.2.i.ba $$4$$ $$20.697$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots$$
2592.2.i.bb $$4$$ $$20.697$$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$$
2592.2.i.bc $$4$$ $$20.697$$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots$$
2592.2.i.bd $$4$$ $$20.697$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+\beta _{2}q^{11}+(-3+\cdots)q^{13}+\cdots$$
2592.2.i.be $$4$$ $$20.697$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots$$
2592.2.i.bf $$4$$ $$20.697$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(-3+\cdots)q^{13}+\cdots$$
2592.2.i.bg $$8$$ $$20.697$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$$
2592.2.i.bh $$8$$ $$20.697$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(2592, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2592, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(324, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(648, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(864, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1296, [\chi])$$$$^{\oplus 2}$$