Space of modular forms of level 1040, weight 2, and Character 1040.u

• Label: 1040.2.u
• Level: $1040$
• Weight: $2$
• Character orbit: 1040.u
• Rep. character: $\chi_{1040}(31,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).

	Total	New	Old
Modular forms	360	56	304
Cusp forms	312	56	256
Eisenstein series	48	0	48

Trace form

\( 56 q - 56 q^{9} + 16 q^{21} - 16 q^{37} - 24 q^{41} + 48 q^{53} + 16 q^{57} - 48 q^{61} + 24 q^{65} - 16 q^{73} + 56 q^{81} + 24 q^{89} - 112 q^{93} - 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1040.2.u.a	$1040$	$2$	1040.u	52.f	$4$	$24$	$12$	$8.304$		None		✓			1040.2.u.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1040.2.u.b	$1040$	$2$	1040.u	52.f	$4$	$32$	$16$	$8.304$		None		✓	✓		1040.2.u.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)