Space of modular forms of level 92, weight 2, and trivial character

• Label: 92.2.a
• Level: $92$
• Weight: $2$
• Character orbit: 92.a
• Rep. character: $\chi_{92}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(92))\).

	Total	New	Old
Modular forms	15	2	13
Cusp forms	10	2	8
Eisenstein series	5	0	5

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	Dim
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(1\)

Trace form

\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(92))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
92.2.a.a	$92$	$2$	92.a	1.a	$1$	$1$	$1$	$0.735$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
92.2.a.b	$92$	$2$	92.a	1.a	$1$	$1$	$1$	$0.735$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(92))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(92)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)