Space of modular forms of level 3920, weight 1, and Character 3920.j

• Label: 3920.1.j
• Level: $3920$
• Weight: $1$
• Character orbit: 3920.j
• Rep. character: $\chi_{3920}(3039,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3920.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3920, [\chi])\).

	Total	New	Old
Modular forms	86	11	75
Cusp forms	38	11	27
Eisenstein series	48	0	48

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	11	0	0	0

Trace form

\( 11 q + q^{5} + 13 q^{9} - q^{25} - 2 q^{29} + 2 q^{41} - q^{45} + 2 q^{61} + 11 q^{81} - 2 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3920.1.j.a	$3920$	$1$	3920.j	20.d	$2$	$1$	$1$	$1.956$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	✓				80.1.h.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{5}-q^{9}+q^{25}+2q^{29}+2q^{41}+\cdots\)
3920.1.j.b	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None	✓				560.1.bt.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{15}-\beta q^{23}+\cdots\)
3920.1.j.c	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{35}) \)		✓			3920.1.j.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{5}-q^{9}+2 i q^{13}+2 i q^{17}+\cdots\)
3920.1.j.d	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None	✓				560.1.bt.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{3}+q^{5}+2q^{9}-\beta q^{15}+\beta q^{23}+\cdots\)
3920.1.j.e	$3920$	$1$	3920.j	20.d	$2$	$4$	$4$	$1.956$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-35}) \)	None		✓	✓		3920.1.j.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-\zeta_{12}^{3}q^{5}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3920, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)