Space of modular forms of level 672, weight 2, and Character 672.j

• Label: 672.2.j
• Level: $672$
• Weight: $2$
• Character orbit: 672.j
• Rep. character: $\chi_{672}(239,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $256$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).

	Total	New	Old
Modular forms	144	24	120
Cusp forms	112	24	88
Eisenstein series	32	0	32

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.2.j.a	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.j.b	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
672.2.j.c	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
672.2.j.d	$672$	$2$	672.j	24.f	$2$	$12$	$12$	$5.366$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)