Space of modular forms of level 110, weight 2, and trivial character

• Label: 110.2.a
• Level: $110$
• Weight: $2$
• Character orbit: 110.a
• Rep. character: $\chi_{110}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(110))\).

	Total	New	Old
Modular forms	22	5	17
Cusp forms	15	5	10
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(1\)
Plus space			\(+\)	\(0\)
Minus space			\(-\)	\(5\)

Trace form

5 * q - q^2 + 5 * q^4 + q^5 + 8 * q^7 - q^8 + 5 * q^9 - q^10 - q^11 + 2 * q^13 - 4 * q^14 - 4 * q^15 + 5 * q^16 - 10 * q^17 - 13 * q^18 + 4 * q^19 + q^20 - 16 * q^21 + q^22 - 12 * q^23 + 5 * q^25 - 10 * q^26 - 24 * q^27 + 8 * q^28 - 10 * q^29 - 4 * q^31 - q^32 - 10 * q^34 + 5 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^39 - q^40 + 2 * q^41 + 8 * q^42 + 12 * q^43 - q^44 + 13 * q^45 + 12 * q^46 + 4 * q^47 + 17 * q^49 - q^50 - 8 * q^51 + 2 * q^52 + 14 * q^53 + 24 * q^54 - q^55 - 4 * q^56 + 2 * q^58 - 4 * q^59 - 4 * q^60 + 6 * q^61 + 8 * q^62 + 8 * q^63 + 5 * q^64 - 6 * q^65 - 4 * q^66 + 40 * q^67 - 10 * q^68 - 24 * q^69 + 8 * q^70 + 4 * q^71 - 13 * q^72 - 2 * q^73 + 2 * q^74 + 4 * q^76 + 8 * q^77 + 8 * q^78 + q^80 + 29 * q^81 - 10 * q^82 - 12 * q^83 - 16 * q^84 - 10 * q^85 + 12 * q^86 - 32 * q^87 + q^88 - 18 * q^89 - 13 * q^90 - 8 * q^91 - 12 * q^92 - 16 * q^93 + 4 * q^94 + 20 * q^95 - 22 * q^97 - 25 * q^98 - 13 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(110))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	11
110.2.a.a	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	\(\Q\)	None	✓	✓	✓	✓	110.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+5q^{7}+\cdots\)
110.2.a.b	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	\(\Q\)	None	✓	✓	✓	✓	110.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
110.2.a.c	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	\(\Q\)	None	✓	✓	✓	✓	110.2.a.c	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
110.2.a.d	$110$	$2$	110.a	1.a	$1$	$2$	$2$	$0.878$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓	✓	110.2.a.d	$1$	$0$	\(-2\)	\(-1\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(110))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(110)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)