Space of modular forms of level 110, weight 4, and Character 110.f

• Label: 110.4.f
• Level: $110$
• Weight: $4$
• Character orbit: 110.f
• Rep. character: $\chi_{110}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(110, [\chi])\).

	Total	New	Old
Modular forms	116	36	80
Cusp forms	100	36	64
Eisenstein series	16	0	16

Trace form

36 * q - 8 * q^3 - 32 * q^5 + 44 * q^11 + 32 * q^12 - 164 * q^15 - 576 * q^16 + 64 * q^20 - 312 * q^22 - 176 * q^23 + 880 * q^25 - 304 * q^26 + 364 * q^27 + 432 * q^31 + 832 * q^33 - 1808 * q^36 + 960 * q^37 + 48 * q^38 - 400 * q^42 - 496 * q^45 + 2100 * q^47 + 128 * q^48 - 60 * q^53 - 1276 * q^55 + 64 * q^56 - 1344 * q^58 + 160 * q^60 + 1568 * q^66 + 1000 * q^67 + 3456 * q^70 - 1312 * q^71 + 3196 * q^75 - 4088 * q^77 + 5312 * q^78 + 512 * q^80 - 10436 * q^81 - 1280 * q^82 - 1472 * q^86 - 1248 * q^88 - 2096 * q^91 + 704 * q^92 + 11372 * q^93 - 4224 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(110, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
110.4.f.a	$110$	$4$	110.f	55.e	$4$	$36$	$18$	$6.490$		None		✓	✓	✓	110.4.f.a	$4$	$0$	\(0\)	\(-8\)	\(-32\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

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