Space of modular forms of level 120, weight 1, and Character 120.i

• Label: 120.1.i
• Level: $120$
• Weight: $1$
• Character orbit: 120.i
• Rep. character: $\chi_{120}(29,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	120.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(120, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 2 q^{15} + 2 q^{16} + 2 q^{24} - 2 q^{25} - 4 q^{31} + 2 q^{36} - 2 q^{40} + 2 q^{49} + 2 q^{54} - 2 q^{60} - 2 q^{64} + 4 q^{79} + 2 q^{81} - 2 q^{90} - 2 q^{96}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(120, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)		✓	✓	✓	120.1.i.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{3}-q^{4}+i q^{5}-q^{6}+\cdots\)