# Properties

 Label 1110.2.u Level $1110$ Weight $2$ Character orbit 1110.u Rep. character $\chi_{1110}(191,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $96$ Newform subspaces $6$ Sturm bound $456$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.u (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$456$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1110, [\chi])$$.

Total New Old
Modular forms 472 96 376
Cusp forms 440 96 344
Eisenstein series 32 0 32

## Trace form

 $$96q + O(q^{10})$$ $$96q - 24q^{13} - 96q^{16} + 24q^{19} - 48q^{31} + 16q^{34} + 24q^{37} + 32q^{39} - 24q^{42} + 56q^{43} - 16q^{45} + 112q^{49} + 8q^{51} + 24q^{52} + 24q^{55} - 48q^{57} - 40q^{61} - 48q^{66} - 16q^{69} - 24q^{76} + 32q^{79} + 32q^{81} - 32q^{82} + 48q^{87} - 88q^{93} + 8q^{94} - 40q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1110, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1110.2.u.a $$4$$ $$8.863$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$$
1110.2.u.b $$4$$ $$8.863$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$$
1110.2.u.c $$4$$ $$8.863$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\zeta_{8}^{3}q^{2}+(\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$$
1110.2.u.d $$4$$ $$8.863$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{8}^{3}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$$
1110.2.u.e $$40$$ $$8.863$$ None $$0$$ $$0$$ $$0$$ $$-24$$
1110.2.u.f $$40$$ $$8.863$$ None $$0$$ $$0$$ $$0$$ $$24$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1110, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(111, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(222, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$