Space of modular forms of level 118, weight 2, and trivial character

• Label: 118.2.a
• Level: $118$
• Weight: $2$
• Character orbit: 118.a
• Rep. character: $\chi_{118}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 118 = 2 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	118.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(118))\).

	Total	New	Old
Modular forms	17	4	13
Cusp forms	14	4	10
Eisenstein series	3	0	3

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

\(2\)	\(59\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(6\)	\(0\)	\(6\)		\(5\)	\(0\)	\(5\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(10\)	\(3\)	\(7\)		\(8\)	\(3\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

4 * q + 2 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^9 + 2 * q^12 - 8 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 - 6 * q^19 - 2 * q^20 - 14 * q^21 + 2 * q^22 + 16 * q^23 - 2 * q^25 - 10 * q^26 + 2 * q^27 - 4 * q^28 - 6 * q^29 - 12 * q^30 + 4 * q^31 + 8 * q^34 + 6 * q^35 - 2 * q^36 - 12 * q^37 + 4 * q^38 + 8 * q^39 + 8 * q^41 - 4 * q^42 - 12 * q^43 + 4 * q^45 + 4 * q^47 + 2 * q^48 - 8 * q^50 + 16 * q^51 - 8 * q^52 + 10 * q^53 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 - 12 * q^61 - 8 * q^62 - 10 * q^63 + 4 * q^64 + 12 * q^65 - 8 * q^66 + 16 * q^67 + 2 * q^68 + 20 * q^69 + 12 * q^70 + 10 * q^71 + 12 * q^73 + 14 * q^74 - 4 * q^75 - 6 * q^76 + 8 * q^77 - 8 * q^78 + 12 * q^79 - 2 * q^80 - 20 * q^81 - 16 * q^82 - 24 * q^83 - 14 * q^84 - 12 * q^85 + 18 * q^86 + 6 * q^87 + 2 * q^88 + 16 * q^89 - 12 * q^90 - 16 * q^91 + 16 * q^92 - 28 * q^93 + 12 * q^94 - 38 * q^95 + 24 * q^97 + 8 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(118))\) 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	59
118.2.a.a	$118$	$2$	118.a	1.a	$1$	$1$	$1$	$0.942$	\(\Q\)	None	✓	✓	✓	✓	118.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
118.2.a.b	$118$	$2$	118.a	1.a	$1$	$1$	$1$	$0.942$	\(\Q\)	None	✓	✓	✓	✓	118.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-3q^{7}+\cdots\)
118.2.a.c	$118$	$2$	118.a	1.a	$1$	$1$	$1$	$0.942$	\(\Q\)	None	✓	✓			118.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
118.2.a.d	$118$	$2$	118.a	1.a	$1$	$1$	$1$	$0.942$	\(\Q\)	None	✓	✓			118.2.a.d	$1$	$0$	\(1\)	\(2\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}-3q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(118))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(118)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)