Space of modular forms of level 155, weight 2, and Character 155.b

• Label: 155.2.b
• Level: $155$
• Weight: $2$
• Character orbit: 155.b
• Rep. character: $\chi_{155}(94,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

	Total	New	Old
Modular forms	18	14	4
Cusp forms	14	14	0
Eisenstein series	4	0	4

Trace form

\( 14 q - 12 q^{4} + 4 q^{6} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.2.b.a	$155$	$2$	155.b	5.b	$2$	$4$	$4$	$1.238$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
155.2.b.b	$155$	$2$	155.b	5.b	$2$	$10$	$10$	$1.238$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)