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

• Label: 156.3.n
• Level: $156$
• Weight: $3$
• Character orbit: 156.n
• Rep. character: $\chi_{156}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $6$
• Sturm bound: $84$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(84\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	120	56	64
Cusp forms	104	56	48
Eisenstein series	16	0	16

Trace form

\( 56 q + 84 q^{9} + O(q^{10}) \)

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.n.a	$156$	$3$	156.n	52.i	$6$	$2$	$1$	$4.251$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
156.3.n.b	$156$	$3$	156.n	52.i	$6$	$2$	$1$	$4.251$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
156.3.n.c	$156$	$3$	156.n	52.i	$6$	$4$	$2$	$4.251$	\(\Q(\sqrt{-3}, \sqrt{142})\)	None		$2$	$0$	\(-8\)	\(6\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\)
156.3.n.d	$156$	$3$	156.n	52.i	$6$	$4$	$2$	$4.251$	\(\Q(\sqrt{-3}, \sqrt{142})\)	None		$2$	$0$	\(-4\)	\(-6\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-2\beta _{2})q^{2}+(-2-\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots\)
156.3.n.e	$156$	$3$	156.n	52.i	$6$	$22$	$11$	$4.251$		None		$2$	$0$	\(2\)	\(-33\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{6}]$
156.3.n.f	$156$	$3$	156.n	52.i	$6$	$22$	$11$	$4.251$		None		$2$	$0$	\(10\)	\(33\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)