Space of modular forms of level 110, weight 3, and Character 110.d

• Label: 110.3.d
• Level: $110$
• Weight: $3$
• Character orbit: 110.d
• Rep. character: $\chi_{110}(21,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(110, [\chi])\).

	Total	New	Old
Modular forms	40	8	32
Cusp forms	32	8	24
Eisenstein series	8	0	8

Trace form

8 * q - 8 * q^3 - 16 * q^4 + 40 * q^9 + 16 * q^12 - 32 * q^14 - 40 * q^15 + 32 * q^16 - 136 * q^23 + 40 * q^25 + 80 * q^26 + 64 * q^27 - 64 * q^31 + 88 * q^33 + 112 * q^34 - 80 * q^36 - 48 * q^37 - 208 * q^42 + 152 * q^47 - 32 * q^48 - 232 * q^49 + 352 * q^53 + 64 * q^56 - 64 * q^58 + 80 * q^59 + 80 * q^60 - 64 * q^64 - 176 * q^66 + 24 * q^67 + 112 * q^69 - 256 * q^71 - 40 * q^75 - 440 * q^77 + 224 * q^78 + 88 * q^81 + 368 * q^82 + 32 * q^86 - 368 * q^89 + 240 * q^91 + 272 * q^92 - 272 * q^93 - 32 * q^97 + 704 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(110, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
110.3.d.a	$110$	$3$	110.d	11.b	$2$	$8$	$8$	$2.997$	8.0.4956160000.2	None		✓	✓	✓	110.3.d.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}-2q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(110, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)