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

• Label: 148.1.p
• Level: $148$
• Weight: $1$
• Character orbit: 148.p
• Rep. character: $\chi_{148}(7,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• 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.p (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{18})\)
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	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

6 * q - 3 * q^5 - 3 * q^8 - 3 * q^17 - 3 * q^20 - 3 * q^25 + 3 * q^26 - 3 * q^34 + 6 * q^36 + 6 * q^40 - 3 * q^41 + 6 * q^50 - 3 * q^58 + 6 * q^61 - 3 * q^64 + 3 * q^65 - 6 * q^73 - 3 * q^74 + 3 * q^85 + 6 * q^89 - 3 * q^90

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.p.a	$148$	$1$	148.p	148.p	$18$	$6$	$1$	$0.074$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	148.1.p.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots\)