Space of modular forms of level 296, weight 2, and trivial character

• Label: 296.2.a
• Level: $296$
• Weight: $2$
• Character orbit: 296.a
• Rep. character: $\chi_{296}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $76$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(76\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(296))\).

	Total	New	Old
Modular forms	42	9	33
Cusp forms	35	9	26
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.

\(2\)	\(37\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(7\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(296))\) 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	37
296.2.a.a	$296$	$2$	296.a	1.a	$1$	$1$	$1$	$2.364$	\(\Q\)	None	✓	✓	✓	✓	296.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
296.2.a.b	$296$	$2$	296.a	1.a	$1$	$1$	$1$	$2.364$	\(\Q\)	None	✓	✓	✓	✓	296.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}-2q^{9}-3q^{11}+2q^{17}+\cdots\)
296.2.a.c	$296$	$2$	296.a	1.a	$1$	$3$	$3$	$2.364$	3.3.229.1	None	✓	✓	✓	✓	296.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
296.2.a.d	$296$	$2$	296.a	1.a	$1$	$4$	$4$	$2.364$	4.4.48389.1	None	✓	✓	✓	✓	296.2.a.d	$1$	$0$	\(0\)	\(2\)	\(5\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(296))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(296)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 2}\)