Space of modular forms of level 1360, weight 2, and Character 1360.bn

• Label: 1360.2.bn
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.bn
• Rep. character: $\chi_{1360}(783,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bn (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1360, [\chi])\).

	Total	New	Old
Modular forms	456	96	360
Cusp forms	408	96	312
Eisenstein series	48	0	48

Trace form

\( 96 q + 48 q^{21} - 48 q^{33} - 48 q^{41} + 48 q^{53} + 96 q^{57} + 96 q^{65} + 48 q^{73} - 144 q^{81} - 48 q^{93} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1360, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1360.2.bn.a	$1360$	$2$	1360.bn	20.e	$4$	$32$	$16$	$10.860$		None		✓			1360.2.bn.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1360.2.bn.b	$1360$	$2$	1360.bn	20.e	$4$	$64$	$32$	$10.860$		None		✓	✓		1360.2.bn.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 3}\)