# Properties

 Label 1110.2.i Level $1110$ Weight $2$ Character orbit 1110.i Rep. character $\chi_{1110}(121,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $56$ Newform subspaces $16$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$16$$ Sturm bound: $$456$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 472 56 416
Cusp forms 440 56 384
Eisenstein series 32 0 32

## Trace form

 $$56q - 4q^{3} - 28q^{4} + 4q^{7} - 28q^{9} + O(q^{10})$$ $$56q - 4q^{3} - 28q^{4} + 4q^{7} - 28q^{9} + 8q^{10} - 8q^{11} - 4q^{12} + 4q^{13} + 16q^{14} - 28q^{16} - 16q^{17} + 4q^{19} + 4q^{21} - 16q^{23} - 28q^{25} - 8q^{26} + 8q^{27} + 4q^{28} + 16q^{29} - 4q^{30} + 24q^{31} + 12q^{34} + 56q^{36} + 16q^{38} + 16q^{39} - 4q^{40} - 32q^{41} + 8q^{42} + 8q^{43} + 4q^{44} - 12q^{46} + 32q^{47} + 8q^{48} - 24q^{49} - 32q^{51} + 4q^{52} - 8q^{53} - 12q^{55} - 8q^{56} - 24q^{57} - 24q^{58} - 20q^{59} + 8q^{61} - 8q^{63} + 56q^{64} + 4q^{65} - 8q^{66} + 12q^{67} + 32q^{68} + 16q^{69} - 8q^{70} + 24q^{71} + 8q^{73} - 12q^{74} + 8q^{75} + 4q^{76} + 40q^{77} - 8q^{78} - 44q^{79} - 28q^{81} - 16q^{82} + 16q^{83} - 8q^{84} + 8q^{86} - 8q^{87} - 12q^{89} - 4q^{90} - 20q^{91} + 8q^{92} + 28q^{93} + 8q^{94} - 16q^{95} - 56q^{97} + 16q^{98} + 4q^{99} + O(q^{100})$$

## 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.i.a $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$1$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
1110.2.i.b $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-1$$ $$-3$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
1110.2.i.c $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
1110.2.i.d $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
1110.2.i.e $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-1$$ $$3$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
1110.2.i.f $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
1110.2.i.g $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
1110.2.i.h $$2$$ $$8.863$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
1110.2.i.i $$4$$ $$8.863$$ $$\Q(\sqrt{-3}, \sqrt{145})$$ None $$-2$$ $$-2$$ $$2$$ $$-2$$ $$q+(-1+\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots$$
1110.2.i.j $$4$$ $$8.863$$ $$\Q(\sqrt{-3}, \sqrt{73})$$ None $$-2$$ $$2$$ $$-2$$ $$0$$ $$q-\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$$
1110.2.i.k $$4$$ $$8.863$$ $$\Q(\sqrt{-3}, \sqrt{41})$$ None $$2$$ $$-2$$ $$-2$$ $$6$$ $$q+(1-\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}-\beta _{2}q^{5}+\cdots$$
1110.2.i.l $$4$$ $$8.863$$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$2$$ $$-2$$ $$2$$ $$-2$$ $$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$$
1110.2.i.m $$4$$ $$8.863$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$-2$$ $$2$$ $$-1$$ $$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$$
1110.2.i.n $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$2$$ $$2$$ $$-2$$ $$-2$$ $$q+(1-\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots$$
1110.2.i.o $$6$$ $$8.863$$ 6.0.45911232.1 None $$-3$$ $$3$$ $$3$$ $$-1$$ $$q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots$$
1110.2.i.p $$10$$ $$8.863$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-5$$ $$-5$$ $$-5$$ $$0$$ $$q+(-1-\beta _{6})q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+\beta _{6}q^{5}+\cdots$$

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

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