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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(8\)	\(1\)	\(7\)		\(7\)	\(1\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(13\)	\(4\)	\(9\)		\(11\)	\(4\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(13\)	\(3\)	\(10\)		\(11\)	\(3\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(8\)	\(1\)	\(7\)		\(6\)	\(1\)	\(5\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(16\)	\(2\)	\(14\)		\(13\)	\(2\)	\(11\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(26\)	\(7\)	\(19\)		\(22\)	\(7\)	\(15\)		\(4\)	\(0\)	\(4\)

Trace form

9 * q + 2 * q^3 + 2 * q^5 + 4 * q^7 + 7 * q^9 + 2 * q^11 + 2 * q^13 + 12 * q^15 + 2 * q^17 - 3 * q^25 + 8 * q^27 - 2 * q^29 + 8 * q^31 - 4 * q^33 - 24 * q^35 + q^37 - 16 * q^39 + 8 * q^43 + 6 * q^45 - 8 * q^47 + 13 * q^49 - 12 * q^51 - 2 * q^53 - 16 * q^55 - 32 * q^57 - 16 * q^59 + 14 * q^61 - 12 * q^63 + 6 * q^67 - 24 * q^69 - 20 * q^71 - 4 * q^73 + 4 * q^75 - 32 * q^77 + 4 * q^79 - 31 * q^81 + 8 * q^83 + 4 * q^85 - 20 * q^87 - 18 * q^89 + 20 * q^91 + 24 * q^93 - 36 * q^95 - 18 * q^97 + 24 * q^99

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

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