Space of modular forms of level 114, weight 2, and trivial character

• Label: 114.2.a
• Level: $114$
• Weight: $2$
• Character orbit: 114.a
• Rep. character: $\chi_{114}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(114))\).

	Total	New	Old
Modular forms	24	3	21
Cusp forms	17	3	14
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.

\(2\)	\(3\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(10\)	\(0\)	\(10\)		\(7\)	\(0\)	\(7\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(14\)	\(3\)	\(11\)		\(10\)	\(3\)	\(7\)		\(4\)	\(0\)	\(4\)

Trace form

3 * q + q^2 - q^3 + 3 * q^4 + 2 * q^5 + q^6 + q^8 + 3 * q^9 + 2 * q^10 - q^12 - 2 * q^13 - 8 * q^14 - 2 * q^15 + 3 * q^16 - 2 * q^17 + q^18 + q^19 + 2 * q^20 - 8 * q^21 - 8 * q^22 - 12 * q^23 + q^24 - 11 * q^25 - 2 * q^26 - q^27 - 2 * q^29 - 2 * q^30 + 12 * q^31 + q^32 + 2 * q^34 + 3 * q^36 - 2 * q^37 - q^38 - 6 * q^39 + 2 * q^40 + 26 * q^41 - 12 * q^43 + 2 * q^45 - 8 * q^46 + 12 * q^47 - q^48 + 11 * q^49 - q^50 + 14 * q^51 - 2 * q^52 - 2 * q^53 + q^54 - 8 * q^55 - 8 * q^56 + q^57 + 10 * q^58 + 4 * q^59 - 2 * q^60 + 18 * q^61 + 3 * q^64 + 4 * q^65 + 8 * q^66 - 4 * q^67 - 2 * q^68 - 8 * q^71 + q^72 + 6 * q^73 + 14 * q^74 + q^75 + q^76 + 16 * q^77 - 6 * q^78 - 4 * q^79 + 2 * q^80 + 3 * q^81 + 6 * q^82 - 16 * q^83 - 8 * q^84 - 12 * q^85 + 12 * q^86 + 14 * q^87 - 8 * q^88 - 14 * q^89 + 2 * q^90 + 16 * q^91 - 12 * q^92 - 8 * q^93 - 8 * q^94 - 2 * q^95 + q^96 - 10 * q^97 - 7 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(114))\) 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	3	19
114.2.a.a	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	\(\Q\)	None	✓	✓	✓	✓	114.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
114.2.a.b	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	\(\Q\)	None	✓	✓	✓	✓	114.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
114.2.a.c	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	\(\Q\)	None	✓	✓	✓	✓	114.2.a.c	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(114)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)