Space of modular forms of level 736, weight 2, and Character 736.x

• Label: 736.2.x
• Level: $736$
• Weight: $2$
• Character orbit: 736.x
• Rep. character: $\chi_{736}(49,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $220$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.x (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(736, [\chi])\).

	Total	New	Old
Modular forms	1040	260	780
Cusp forms	880	220	660
Eisenstein series	160	40	120

Trace form

220 * q + 22 * q^7 + 22 * q^15 - 18 * q^17 + 16 * q^23 - 4 * q^25 + 34 * q^31 - 30 * q^33 + 18 * q^39 - 18 * q^41 + 40 * q^47 - 28 * q^49 + 38 * q^55 - 30 * q^57 - 18 * q^63 - 38 * q^65 + 26 * q^71 - 18 * q^73 + 22 * q^79 - 52 * q^81 + 42 * q^87 - 2 * q^89 + 78 * q^95 - 18 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(736, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
736.2.x.a	$736$	$2$	736.x	184.p	$22$	$220$	$22$	$5.877$		None			✓	✓	184.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(22\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(736, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 3}\)