Space of modular forms of level 156, weight 3, and Character 156.s

• Label: 156.3.s
• Level: $156$
• Weight: $3$
• Character orbit: 156.s
• Rep. character: $\chi_{156}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(156, [\chi])\).

	Total	New	Old
Modular forms	124	18	106
Cusp forms	100	18	82
Eisenstein series	24	0	24

Trace form

\( 18 q + 3 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(156, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.3.s.a	$156$	$3$	156.s	39.h	$6$	$2$	$1$	$4.251$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-15\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-3+3\zeta_{6})q^{3}+(-10+5\zeta_{6})q^{7}+\cdots\)
156.3.s.b	$156$	$3$	156.s	39.h	$6$	$16$	$8$	$4.251$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(18\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{8}q^{3}+\beta _{2}q^{5}+(2+\beta _{12}+\beta _{13}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)