Space of modular forms of level 1920, weight 1, and Character 1920.i

• Label: 1920.1.i
• Level: $1920$
• Weight: $1$
• Character orbit: 1920.i
• Rep. character: $\chi_{1920}(449,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1920.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1920, [\chi])\).

	Total	New	Old
Modular forms	56	8	48
Cusp forms	24	8	16
Eisenstein series	32	0	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 8 q^{25} - 8 q^{49} + 8 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1920, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1920.1.i.a	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \)	\(\Q(\sqrt{6}) \)	✓	✓			1920.1.i.a	$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q-q^{3}-q^{5}+q^{9}+q^{15}-2q^{23}+q^{25}+\cdots\)
1920.1.i.b	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \)	\(\Q(\sqrt{6}) \)	✓	✓			1920.1.i.a	$4$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{3}+q^{5}+q^{9}-q^{15}+2q^{23}+q^{25}+\cdots\)
1920.1.i.c	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \)	\(\Q(\sqrt{6}) \)	✓	✓			1920.1.i.a	$4$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+q^{3}-q^{5}+q^{9}-q^{15}+2q^{23}+q^{25}+\cdots\)
1920.1.i.d	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \)	\(\Q(\sqrt{6}) \)	✓	✓			1920.1.i.a	$4$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{3}+q^{5}+q^{9}+q^{15}-2q^{23}+q^{25}+\cdots\)
1920.1.i.e	$1920$	$1$	1920.i	120.i	$2$	$2$	$2$	$0.958$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{30}) \)		✓			1920.1.i.e	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-i q^{3}-q^{5}-2 i q^{7}-q^{9}+i q^{15}+\cdots\)
1920.1.i.f	$1920$	$1$	1920.i	120.i	$2$	$2$	$2$	$0.958$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{30}) \)		✓			1920.1.i.e	$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-i q^{3}+q^{5}+2 i q^{7}-q^{9}-i q^{15}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1920, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1920, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 3}\)