Space of modular forms of level 252, weight 4, and Character 252.e

• Label: 252.4.e
• Level: $252$
• Weight: $4$
• Character orbit: 252.e
• Rep. character: $\chi_{252}(71,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

	Total	New	Old
Modular forms	152	36	116
Cusp forms	136	36	100
Eisenstein series	16	0	16

Trace form

\( 36 q - 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.4.e.a	$252$	$4$	252.e	12.b	$2$	$36$	$36$	$14.868$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \)