Space of modular forms of level 252, weight 2, and Character 252.bi

• Label: 252.2.bi
• Level: $252$
• Weight: $2$
• Character orbit: 252.bi
• Rep. character: $\chi_{252}(139,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

	Total	New	Old
Modular forms	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

\( 88 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.2.bi.a	$252$	$2$	252.bi	252.ai	$6$	$4$	$2$	$2.012$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(2\zeta_{12}+\cdots)q^{3}+\cdots\)
252.2.bi.b	$252$	$2$	252.bi	252.ai	$6$	$4$	$2$	$2.012$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots\)
252.2.bi.c	$252$	$2$	252.bi	252.ai	$6$	$80$	$40$	$2.012$		None		$8$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$