Space of modular forms of level 296, weight 2, and Character 296.u

• Label: 296.2.u
• Level: $296$
• Weight: $2$
• Character orbit: 296.u
• Rep. character: $\chi_{296}(9,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $54$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

	Total	New	Old
Modular forms	252	54	198
Cusp forms	204	54	150
Eisenstein series	48	0	48

Trace form

\( 54 q - 3 q^{5} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
296.2.u.a	$296$	$2$	296.u	37.f	$9$	$24$	$4$	$2.364$		None		✓			296.2.u.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$\mathrm{SU}(2)[C_{9}]$
296.2.u.b	$296$	$2$	296.u	37.f	$9$	$30$	$5$	$2.364$		None		✓	✓		296.2.u.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-3\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(296, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)