Space of modular forms of level 368, weight 2, and Character 368.s

• Label: 368.2.s
• Level: $368$
• Weight: $2$
• Character orbit: 368.s
• Rep. character: $\chi_{368}(15,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.s (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

	Total	New	Old
Modular forms	540	120	420
Cusp forms	420	120	300
Eisenstein series	120	0	120

Trace form

\( 120 q + 12 q^{9} + 12 q^{25} + 24 q^{29} - 24 q^{41} - 36 q^{49} + 24 q^{69} - 72 q^{77} - 204 q^{81} - 156 q^{85} - 132 q^{89} - 24 q^{93} - 132 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.2.s.a	$368$	$2$	368.s	92.h	$22$	$40$	$4$	$2.938$		None		✓			368.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
368.2.s.b	$368$	$2$	368.s	92.h	$22$	$80$	$8$	$2.938$		None		✓	✓		368.2.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)