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

• Label: 110.2.f
• Level: $110$
• Weight: $2$
• Character orbit: 110.f
• Rep. character: $\chi_{110}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	44	12	32
Cusp forms	28	12	16
Eisenstein series	16	0	16

Trace form

12 * q + 4 * q^3 + 8 * q^5 - 12 * q^11 - 4 * q^12 - 4 * q^15 - 12 * q^16 + 4 * q^20 + 4 * q^22 - 12 * q^23 - 20 * q^25 - 8 * q^26 - 8 * q^27 - 16 * q^31 + 4 * q^33 + 4 * q^36 - 20 * q^37 - 24 * q^38 + 40 * q^42 + 44 * q^45 + 20 * q^47 - 4 * q^48 + 60 * q^53 - 16 * q^55 + 8 * q^56 + 32 * q^58 + 20 * q^60 + 16 * q^66 - 20 * q^67 + 16 * q^70 + 56 * q^71 - 84 * q^75 + 16 * q^77 - 16 * q^78 - 8 * q^80 + 28 * q^81 - 64 * q^86 + 4 * q^88 - 32 * q^91 + 12 * q^92 - 56 * q^93 - 12 * q^97

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.f.a	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	\(\Q(\zeta_{8})\)	None		✓			110.2.f.a	$4$	$0$	\(0\)	\(-4\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.b	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	\(\Q(\zeta_{8})\)	None		✓			110.2.f.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(1-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
110.2.f.c	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	\(\Q(\zeta_{8})\)	None		✓			110.2.f.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)

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

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