# Properties

 Label 1120.2.q Level $1120$ Weight $2$ Character orbit 1120.q Rep. character $\chi_{1120}(641,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $64$ Newform subspaces $11$ Sturm bound $384$ Trace bound $7$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1120 = 2^{5} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1120.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$11$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1120, [\chi])$$.

Total New Old
Modular forms 416 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

## Trace form

 $$64q - 32q^{9} + O(q^{10})$$ $$64q - 32q^{9} + 32q^{13} - 40q^{21} - 32q^{25} - 16q^{29} - 16q^{37} - 16q^{41} + 8q^{45} + 32q^{49} + 16q^{53} + 32q^{57} + 48q^{61} + 8q^{65} - 32q^{69} - 16q^{73} + 48q^{77} - 56q^{81} - 40q^{89} + 16q^{93} - 64q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1120, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1120.2.q.a $$2$$ $$8.943$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$-4$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
1120.2.q.b $$2$$ $$8.943$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$$
1120.2.q.c $$2$$ $$8.943$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
1120.2.q.d $$2$$ $$8.943$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-1$$ $$4$$ $$q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1120.2.q.e $$4$$ $$8.943$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$$
1120.2.q.f $$4$$ $$8.943$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$2$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
1120.2.q.g $$8$$ $$8.943$$ 8.0.49787136.1 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{4}q^{3}+(-1+\beta _{2})q^{5}-\beta _{7}q^{7}+2\beta _{4}q^{11}+\cdots$$
1120.2.q.h $$8$$ $$8.943$$ 8.0.1445900625.1 None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{7}q^{3}-\beta _{3}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots$$
1120.2.q.i $$10$$ $$8.943$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$5$$ $$-2$$ $$q-\beta _{5}q^{3}+(1-\beta _{1})q^{5}+\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots$$
1120.2.q.j $$10$$ $$8.943$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$5$$ $$2$$ $$q+\beta _{5}q^{3}+(1-\beta _{1})q^{5}-\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots$$
1120.2.q.k $$12$$ $$8.943$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{2}q^{5}+\beta _{9}q^{7}+(\beta _{1}+2\beta _{2}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1120, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1120, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 2}$$