Space of modular forms of level 1110, weight 2, and Character 1110.i

• 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: $7$

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

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1110.2.i.a	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.a	$2$	$0$	$-1$	$-1$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1110.2.i.b	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.b	$2$	$1$	$-1$	$1$	$-1$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1110.2.i.c	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.c	$2$	$0$	$1$	$-1$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1110.2.i.d	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.d	$2$	$0$	$1$	$-1$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1110.2.i.e	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.e	$2$	$0$	$1$	$1$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1110.2.i.f	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.f	$2$	$0$	$1$	$1$	$1$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1110.2.i.g	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.g	$2$	$0$	$1$	$1$	$1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1110.2.i.h	$1110$	$2$	1110.i	37.c	$3$	$2$	$1$	$8.863$	$\Q(\sqrt{-3})$	None		✓			1110.2.i.h	$2$	$0$	$1$	$1$	$1$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1110.2.i.i	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\sqrt{-3}, \sqrt{145})$	None		✓			1110.2.i.i	$2$	$0$	$-2$	$-2$	$2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots$
1110.2.i.j	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\sqrt{-3}, \sqrt{73})$	None		✓			1110.2.i.j	$2$	$0$	$-2$	$2$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$
1110.2.i.k	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\sqrt{-3}, \sqrt{41})$	None		✓			1110.2.i.k	$2$	$0$	$2$	$-2$	$-2$	$6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}-\beta _{2}q^{5}+\cdots$
1110.2.i.l	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\sqrt{-3}, \sqrt{-5})$	None		✓			1110.2.i.l	$2$	$0$	$2$	$-2$	$2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$
1110.2.i.m	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			1110.2.i.m	$2$	$0$	$2$	$-2$	$2$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$
1110.2.i.n	$1110$	$2$	1110.i	37.c	$3$	$4$	$2$	$8.863$	$\Q(\zeta_{12})$	None		✓			1110.2.i.n	$2$	$0$	$2$	$2$	$-2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_1+1)q^{2}+\beta_1 q^{3}-\beta_1 q^{4}+\cdots$
1110.2.i.o	$1110$	$2$	1110.i	37.c	$3$	$6$	$3$	$8.863$	6.0.45911232.1	None		✓			1110.2.i.o	$2$	$0$	$-3$	$3$	$3$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots$
1110.2.i.p	$1110$	$2$	1110.i	37.c	$3$	$10$	$5$	$8.863$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		1110.2.i.p	$2$	$0$	$-5$	$-5$	$-5$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{6})q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+\beta _{6}q^{5}+\cdots$

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

$S_{2}^{\mathrm{old}}(1110, [\chi]) \simeq$ $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}$