# Properties

 Label 1110.2.x Level $1110$ Weight $2$ Character orbit 1110.x Rep. character $\chi_{1110}(751,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $5$ Sturm bound $456$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.x (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$456$$ Trace bound: $$13$$ 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 56 416
Cusp forms 440 56 384
Eisenstein series 32 0 32

## Trace form

 $$56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} + O(q^{10})$$ $$56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} - 8q^{10} - 8q^{11} + 4q^{12} - 12q^{13} - 28q^{16} - 12q^{19} - 4q^{21} + 28q^{25} - 8q^{26} + 8q^{27} + 4q^{28} - 4q^{30} + 16q^{33} + 12q^{34} + 24q^{35} - 56q^{36} + 16q^{37} + 16q^{38} + 24q^{39} - 4q^{40} + 24q^{42} - 4q^{44} - 4q^{46} + 32q^{47} + 8q^{48} - 56q^{49} - 12q^{52} - 8q^{53} - 12q^{55} - 24q^{58} + 36q^{59} + 8q^{63} - 56q^{64} + 4q^{65} - 12q^{67} + 8q^{70} + 8q^{71} - 8q^{73} - 12q^{74} - 8q^{75} - 12q^{76} - 8q^{77} - 8q^{78} + 12q^{79} - 28q^{81} + 48q^{83} - 8q^{84} + 32q^{85} - 8q^{86} + 24q^{87} + 36q^{89} + 4q^{90} - 12q^{91} - 24q^{92} - 84q^{93} + 24q^{94} - 16q^{95} - 48q^{98} + 4q^{99} + O(q^{100})$$

## 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.x.a $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$2$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots$$
1110.2.x.b $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$2$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots$$
1110.2.x.c $$16$$ $$8.863$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-8$$ $$0$$ $$-2$$ $$q+(-\beta _{6}+\beta _{10})q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\cdots$$
1110.2.x.d $$16$$ $$8.863$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-8$$ $$0$$ $$-2$$ $$q+(\beta _{3}+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{9}q^{4}+\beta _{3}q^{5}+\cdots$$
1110.2.x.e $$16$$ $$8.863$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$-4$$ $$q+\beta _{6}q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{7}q^{5}+\cdots$$

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

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