# Properties

 Label 1110.2.d Level $1110$ Weight $2$ Character orbit 1110.d Rep. character $\chi_{1110}(889,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $10$ Sturm bound $456$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$456$$ Trace bound: $$6$$ 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 236 36 200
Cusp forms 220 36 184
Eisenstein series 16 0 16

## Trace form

 $$36 q - 36 q^{4} + 8 q^{5} - 4 q^{6} - 36 q^{9} + O(q^{10})$$ $$36 q - 36 q^{4} + 8 q^{5} - 4 q^{6} - 36 q^{9} + 4 q^{10} - 16 q^{11} - 4 q^{15} + 36 q^{16} + 24 q^{19} - 8 q^{20} + 4 q^{24} - 20 q^{25} + 32 q^{29} - 8 q^{31} - 16 q^{35} + 36 q^{36} - 4 q^{40} + 16 q^{44} - 8 q^{45} - 12 q^{49} - 8 q^{51} + 4 q^{54} - 16 q^{55} - 16 q^{59} + 4 q^{60} - 24 q^{61} - 36 q^{64} + 24 q^{65} - 16 q^{66} + 32 q^{69} + 24 q^{70} - 16 q^{71} - 24 q^{76} + 56 q^{79} + 8 q^{80} + 36 q^{81} - 24 q^{85} - 48 q^{86} - 4 q^{90} - 64 q^{91} + 64 q^{94} - 32 q^{95} - 4 q^{96} + 16 q^{99} + O(q^{100})$$

## 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.d.a $2$ $8.863$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(-2-i)q^{5}+\cdots$$
1110.2.d.b $2$ $8.863$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots$$
1110.2.d.c $2$ $8.863$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots$$
1110.2.d.d $2$ $8.863$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots$$
1110.2.d.e $2$ $8.863$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots$$
1110.2.d.f $4$ $8.863$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-q^{6}+\cdots$$
1110.2.d.g $4$ $8.863$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$$
1110.2.d.h $4$ $8.863$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$$
1110.2.d.i $6$ $8.863$ 6.0.5161984.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{4}q^{2}-\beta _{4}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
1110.2.d.j $8$ $8.863$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(370, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$