# Properties

 Label 1110.2.h Level $1110$ Weight $2$ Character orbit 1110.h Rep. character $\chi_{1110}(961,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $7$ 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.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$456$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 236 28 208
Cusp forms 220 28 192
Eisenstein series 16 0 16

## Trace form

 $$28q + 4q^{3} - 28q^{4} - 8q^{7} + 28q^{9} + O(q^{10})$$ $$28q + 4q^{3} - 28q^{4} - 8q^{7} + 28q^{9} - 4q^{10} + 8q^{11} - 4q^{12} + 28q^{16} - 8q^{21} - 28q^{25} + 8q^{26} + 4q^{27} + 8q^{28} + 4q^{30} + 8q^{33} + 24q^{34} - 28q^{36} + 20q^{37} + 8q^{38} + 4q^{40} - 8q^{44} - 8q^{46} + 16q^{47} + 4q^{48} - 4q^{49} + 8q^{53} + 24q^{58} - 24q^{62} - 8q^{63} - 28q^{64} + 8q^{65} - 8q^{70} + 16q^{71} + 32q^{73} - 12q^{74} - 4q^{75} - 16q^{77} + 8q^{78} + 28q^{81} + 48q^{83} + 8q^{84} - 8q^{85} + 8q^{86} - 4q^{90} + 16q^{95} + 8q^{99} + O(q^{100})$$

## 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.h.a $$2$$ $$8.863$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$-2$$ $$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-q^{7}+\cdots$$
1110.2.h.b $$2$$ $$8.863$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+2q^{7}+\cdots$$
1110.2.h.c $$2$$ $$8.863$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$2$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+q^{7}+\cdots$$
1110.2.h.d $$4$$ $$8.863$$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots$$
1110.2.h.e $$4$$ $$8.863$$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$-4$$ $$0$$ $$2$$ $$q+\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots$$
1110.2.h.f $$6$$ $$8.863$$ 6.0.279290944.1 None $$0$$ $$6$$ $$0$$ $$-6$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots$$
1110.2.h.g $$8$$ $$8.863$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(74, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(111, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(222, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(370, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$