Space of modular forms of level 156, weight 2, and Character 156.i

• Label: 156.2.i
• Level: $156$
• Weight: $2$
• Character orbit: 156.i
• Rep. character: $\chi_{156}(61,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).

	Total	New	Old
Modular forms	68	2	66
Cusp forms	44	2	42
Eisenstein series	24	0	24

Trace form

\( 2 q + q^{3} + 4 q^{5} - q^{7} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.2.i.a	$156$	$2$	156.i	13.c	$3$	$2$	$1$	$1.246$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)