Space of modular forms of level 148, weight 1, and Character 148.f

• Label: 148.1.f
• Level: $148$
• Weight: $1$
• Character orbit: 148.f
• Rep. character: $\chi_{148}(105,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $19$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	148.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(19\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(148, [\chi])\).

	Total	New	Old
Modular forms	8	2	6
Cusp forms	2	2	0
Eisenstein series	6	0	6

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

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

Trace form

\( 2 q - 2 q^{7} - 2 q^{17} + 2 q^{19} - 2 q^{23} - 2 q^{29} + 2 q^{33} + 2 q^{47} + 2 q^{51} + 2 q^{53} - 2 q^{57} + 2 q^{69} + 2 q^{71} + 2 q^{75} - 2 q^{79} - 2 q^{81} - 2 q^{83} - 2 q^{87} - 2 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(148, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		✓	✓	✓	148.1.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+i q^{3}-q^{7}-i q^{11}+(-i-1)q^{17}+\cdots\)