Space of modular forms of level 46, weight 2, and trivial character

• Label: 46.2.a
• Level: $46$
• Weight: $2$
• Character orbit: 46.a
• Rep. character: $\chi_{46}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(46))\).

	Total	New	Old
Modular forms	8	1	7
Cusp forms	5	1	4
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.

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(-\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(5\)	\(1\)	\(4\)		\(3\)	\(1\)	\(2\)		\(2\)	\(0\)	\(2\)

Trace form

q - q^2 + q^4 + 4 * q^5 - 4 * q^7 - q^8 - 3 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^13 + 4 * q^14 + q^16 - 2 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 2 * q^22 + q^23 + 11 * q^25 + 2 * q^26 - 4 * q^28 + 2 * q^29 - q^32 + 2 * q^34 - 16 * q^35 - 3 * q^36 - 4 * q^37 + 2 * q^38 - 4 * q^40 + 6 * q^41 + 10 * q^43 + 2 * q^44 - 12 * q^45 - q^46 + 9 * q^49 - 11 * q^50 - 2 * q^52 - 4 * q^53 + 8 * q^55 + 4 * q^56 - 2 * q^58 + 12 * q^59 - 8 * q^61 + 12 * q^63 + q^64 - 8 * q^65 - 10 * q^67 - 2 * q^68 + 16 * q^70 + 3 * q^72 + 6 * q^73 + 4 * q^74 - 2 * q^76 - 8 * q^77 - 12 * q^79 + 4 * q^80 + 9 * q^81 - 6 * q^82 + 14 * q^83 - 8 * q^85 - 10 * q^86 - 2 * q^88 - 6 * q^89 + 12 * q^90 + 8 * q^91 + q^92 - 8 * q^95 + 6 * q^97 - 9 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(46))\) 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	23
46.2.a.a	$46$	$2$	46.a	1.a	$1$	$1$	$1$	$0.367$	\(\Q\)	None	✓	✓	✓	✓	46.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(46)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)