# Properties

 Label 2352.2.q Level $2352$ Weight $2$ Character orbit 2352.q Rep. character $\chi_{2352}(961,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $33$ Sturm bound $896$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$33$$ Sturm bound: $$896$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2352, [\chi])$$.

Total New Old
Modular forms 992 80 912
Cusp forms 800 80 720
Eisenstein series 192 0 192

## Trace form

 $$80q + 2q^{3} - 40q^{9} + O(q^{10})$$ $$80q + 2q^{3} - 40q^{9} - 8q^{11} + 10q^{19} - 20q^{23} - 36q^{25} - 4q^{27} - 32q^{29} - 14q^{31} + 4q^{33} + 16q^{37} - 2q^{39} - 16q^{41} + 20q^{43} + 12q^{47} + 24q^{53} + 56q^{55} + 8q^{57} + 16q^{59} + 8q^{61} + 8q^{65} + 2q^{67} - 16q^{71} - 12q^{73} + 14q^{75} - 22q^{79} - 40q^{81} + 24q^{83} + 32q^{85} - 12q^{87} - 16q^{89} - 16q^{93} + 60q^{95} - 8q^{97} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2352, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2352.2.q.a $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-4$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.b $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-4$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.c $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.d $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.e $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.f $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots$$
2352.2.q.g $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots$$
2352.2.q.h $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4+\cdots)q^{17}+\cdots$$
2352.2.q.i $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.j $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.k $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.l $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.m $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$3$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
2352.2.q.n $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$$
2352.2.q.o $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-2q^{13}+\cdots$$
2352.2.q.p $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots$$
2352.2.q.q $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots$$
2352.2.q.r $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots$$
2352.2.q.s $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots$$
2352.2.q.t $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots$$
2352.2.q.u $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(5-5\zeta_{6})q^{11}+\cdots$$
2352.2.q.v $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots$$
2352.2.q.w $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}-6q^{13}+\cdots$$
2352.2.q.x $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots$$
2352.2.q.y $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$4$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$$
2352.2.q.z $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$4$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots$$
2352.2.q.ba $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$$
2352.2.q.bb $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$4$$ $$0$$ $$q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots$$
2352.2.q.bc $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$4$$ $$0$$ $$q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots$$
2352.2.q.bd $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-4$$ $$0$$ $$q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$$
2352.2.q.be $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-4$$ $$0$$ $$q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$$
2352.2.q.bf $$4$$ $$18.781$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$2$$ $$-1$$ $$0$$ $$q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots$$
2352.2.q.bg $$4$$ $$18.781$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$4$$ $$0$$ $$q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2352, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2352, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(392, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(784, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1176, [\chi])$$$$^{\oplus 2}$$