Space of modular forms of level 126, weight 4, and Character 126.g

• Label: 126.4.g
• Level: $126$
• Weight: $4$
• Character orbit: 126.g
• Rep. character: $\chi_{126}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $7$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

	Total	New	Old
Modular forms	160	20	140
Cusp forms	128	20	108
Eisenstein series	32	0	32

Trace form

\( 20 q - 40 q^{4} - 18 q^{5} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.4.g.a	$126$	$4$	126.g	7.c	$3$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-15\)	\(35\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-15+\cdots)q^{5}+\cdots\)
126.4.g.b	$126$	$4$	126.g	7.c	$3$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-6+6\zeta_{6})q^{5}+\cdots\)
126.4.g.c	$126$	$4$	126.g	7.c	$3$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(7\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
126.4.g.d	$126$	$4$	126.g	7.c	$3$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-9\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-9+9\zeta_{6})q^{5}+\cdots\)
126.4.g.e	$126$	$4$	126.g	7.c	$3$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{193})\)	None		$2$	$0$	\(-4\)	\(0\)	\(7\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
126.4.g.f	$126$	$4$	126.g	7.c	$3$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{193})\)	None		$2$	$0$	\(4\)	\(0\)	\(-7\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
126.4.g.g	$126$	$4$	126.g	7.c	$3$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{1345})\)	None		$2$	$0$	\(4\)	\(0\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)