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

• Label: 672.2.h
• Level: $672$
• Weight: $2$
• Character orbit: 672.h
• Rep. character: $\chi_{672}(575,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $256$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(256\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

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

\( 24 q - 8 q^{9} + O(q^{10}) \)

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.h.a	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.b	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.c	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.d	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.e	$672$	$2$	672.h	12.b	$2$	$8$	$8$	$5.366$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \)