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

• Label: 110.2.g
• Level: $110$
• Weight: $2$
• Character orbit: 110.g
• Rep. character: $\chi_{110}(31,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	88	16	72
Cusp forms	56	16	40
Eisenstein series	32	0	32

Trace form

16 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 - 6 * q^6 + 2 * q^8 - 12 * q^9 - 8 * q^10 - 8 * q^11 + 4 * q^12 - 8 * q^13 + 2 * q^14 - 12 * q^15 - 4 * q^16 + 8 * q^17 + 16 * q^18 - 14 * q^19 + 48 * q^21 + 10 * q^22 + 16 * q^23 - 6 * q^24 - 4 * q^25 - 16 * q^26 - 26 * q^27 - 40 * q^29 + 4 * q^30 - 4 * q^31 - 8 * q^32 + 34 * q^33 - 12 * q^34 + 8 * q^35 - 2 * q^36 - 16 * q^37 + 16 * q^38 - 32 * q^39 + 2 * q^40 - 30 * q^41 - 16 * q^42 + 12 * q^43 + 2 * q^44 - 8 * q^46 + 24 * q^47 + 4 * q^48 + 30 * q^49 + 2 * q^50 + 10 * q^51 + 12 * q^52 + 16 * q^54 - 8 * q^55 + 12 * q^56 + 70 * q^57 + 28 * q^58 + 54 * q^59 + 8 * q^60 - 24 * q^61 + 4 * q^62 - 44 * q^63 - 4 * q^64 - 20 * q^65 + 28 * q^66 - 12 * q^67 + 8 * q^68 - 20 * q^69 - 12 * q^71 - 14 * q^72 - 24 * q^73 - 4 * q^74 - 6 * q^75 + 16 * q^76 - 32 * q^78 + 2 * q^81 - 18 * q^82 - 34 * q^83 - 12 * q^84 + 28 * q^85 + 22 * q^86 - 48 * q^87 - 10 * q^88 + 48 * q^89 + 26 * q^90 + 50 * q^91 - 24 * q^92 - 16 * q^93 - 26 * q^94 + 4 * q^96 - 10 * q^97 - 8 * q^98 + 76 * 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.g.a	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	\(\Q(\zeta_{10})\)	None		✓			110.2.g.a	$2$	$0$	\(-1\)	\(4\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
110.2.g.b	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	\(\Q(\zeta_{10})\)	None		✓			110.2.g.b	$2$	$0$	\(1\)	\(4\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
110.2.g.c	$110$	$2$	110.g	11.c	$5$	$8$	$2$	$0.878$	8.0.682515625.5	None		✓	✓		110.2.g.c	$2$	$0$	\(2\)	\(-4\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

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

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