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

• Label: 672.2.q
• Level: $672$
• Weight: $2$
• Character orbit: 672.q
• Rep. character: $\chi_{672}(193,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $12$
• Sturm bound: $256$
• Trace bound: $7$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	288	32	256
Cusp forms	224	32	192
Eisenstein series	64	0	64

Trace form

\( 32 q - 16 q^{9} + O(q^{10}) \)

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.q.a	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
672.2.q.b	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
672.2.q.c	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.d	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.e	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
672.2.q.f	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
672.2.q.g	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
672.2.q.h	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.i	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.j	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
672.2.q.k	$672$	$2$	672.q	7.c	$3$	$6$	$3$	$5.366$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.q.l	$672$	$2$	672.q	7.c	$3$	$6$	$3$	$5.366$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)