Space of modular forms of level 110, weight 2, and Character 110.b

• Label: 110.2.b
• Level: $110$
• Weight: $2$
• Character orbit: 110.b
• Rep. character: $\chi_{110}(89,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(110, [\chi])\).

	Total	New	Old
Modular forms	22	6	16
Cusp forms	14	6	8
Eisenstein series	8	0	8

Trace form

6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 - 10 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^14 - 4 * q^15 + 6 * q^16 + 16 * q^19 - 2 * q^20 + 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^29 - 4 * q^30 - 12 * q^31 - 8 * q^34 - 8 * q^35 + 10 * q^36 + 16 * q^39 - 4 * q^40 - 36 * q^41 - 2 * q^44 - 34 * q^45 - 12 * q^46 + 22 * q^49 + 24 * q^50 + 48 * q^51 + 16 * q^54 - 6 * q^55 + 4 * q^56 + 4 * q^60 - 36 * q^61 - 6 * q^64 + 16 * q^65 + 8 * q^66 - 32 * q^69 + 16 * q^70 - 20 * q^71 + 16 * q^75 - 16 * q^76 - 16 * q^79 + 2 * q^80 - 2 * q^81 + 8 * q^85 + 8 * q^86 + 8 * q^89 - 20 * q^90 + 24 * q^91 - 20 * q^94 - 4 * q^96 + 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(110, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
110.2.b.a	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	\(\Q(\sqrt{-1}) \)	None		✓			110.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}+(i-2)q^{5}+\cdots\)
110.2.b.b	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	\(\Q(\sqrt{-1}) \)	None		✓			110.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots\)
110.2.b.c	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	\(\Q(\sqrt{-1}) \)	None		✓			110.2.b.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}+(-i+2)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(110, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)