Space of modular forms of level 252, weight 8, and Character 252.f

• Label: 252.8.f
• Level: $252$
• Weight: $8$
• Character orbit: 252.f
• Rep. character: $\chi_{252}(125,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	252.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(252, [\chi])\).

	Total	New	Old
Modular forms	348	20	328
Cusp forms	324	20	304
Eisenstein series	24	0	24

Trace form

\( 20 q - 2468 q^{7} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.8.f.a	$252$	$8$	252.f	21.c	$2$	$20$	$20$	$78.721$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	252.8.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2468\)	$2^{52}\cdot 3^{47}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-123+\beta _{6})q^{7}-\beta _{9}q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)