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

• Label: 110.4.b
• Level: $110$
• Weight: $4$
• Character orbit: 110.b
• Rep. character: $\chi_{110}(89,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	58	14	44
Cusp forms	50	14	36
Eisenstein series	8	0	8

Trace form

14 * q - 56 * q^4 - 4 * q^5 + 8 * q^6 - 126 * q^9 - 56 * q^10 - 22 * q^11 + 200 * q^14 + 146 * q^15 + 224 * q^16 - 288 * q^19 + 16 * q^20 + 184 * q^21 - 32 * q^24 + 200 * q^25 + 56 * q^26 - 404 * q^29 + 440 * q^30 - 184 * q^31 - 368 * q^34 - 700 * q^35 + 504 * q^36 - 912 * q^39 + 224 * q^40 - 76 * q^41 + 88 * q^44 + 458 * q^45 + 504 * q^46 + 718 * q^49 + 304 * q^50 + 168 * q^51 + 352 * q^54 - 396 * q^55 - 800 * q^56 - 228 * q^59 - 584 * q^60 - 1788 * q^61 - 896 * q^64 - 1216 * q^65 - 528 * q^66 + 4172 * q^69 - 32 * q^70 + 4864 * q^71 + 288 * q^74 - 3910 * q^75 + 1152 * q^76 - 1944 * q^79 - 64 * q^80 + 654 * q^81 - 736 * q^84 + 1580 * q^85 - 2496 * q^86 + 3796 * q^89 - 488 * q^90 - 5176 * q^91 + 1032 * q^94 + 6360 * q^95 + 128 * q^96 + 1034 * q^99

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.b.a	$110$	$4$	110.b	5.b	$2$	$2$	$2$	$6.490$	\(\Q(\sqrt{-1}) \)	None		✓			110.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+9 i q^{3}-4 q^{4}+(-5 i-10)q^{5}+\cdots\)
110.4.b.b	$110$	$4$	110.b	5.b	$2$	$4$	$4$	$6.490$	\(\Q(i, \sqrt{89})\)	None		✓			110.4.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-4q^{4}+(3\beta _{2}+\beta _{3})q^{5}+\cdots\)
110.4.b.c	$110$	$4$	110.b	5.b	$2$	$8$	$8$	$6.490$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		110.4.b.c	$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(110, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)