Space of modular forms of level 126, weight 3, and Character 126.b

• Label: 126.3.b
• Level: $126$
• Weight: $3$
• Character orbit: 126.b
• Rep. character: $\chi_{126}(71,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

	Total	New	Old
Modular forms	56	4	52
Cusp forms	40	4	36
Eisenstein series	16	0	16

Trace form

4 * q - 8 * q^4 + 8 * q^10 - 32 * q^13 + 16 * q^16 + 80 * q^19 + 16 * q^22 - 132 * q^25 + 16 * q^31 - 104 * q^34 + 152 * q^37 - 16 * q^40 + 80 * q^43 + 16 * q^46 + 28 * q^49 + 64 * q^52 - 464 * q^55 + 152 * q^58 + 232 * q^61 - 32 * q^64 - 192 * q^67 + 112 * q^70 - 96 * q^73 - 160 * q^76 + 304 * q^79 - 216 * q^82 + 328 * q^85 - 32 * q^88 + 112 * q^91 - 96 * q^94 - 288 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.3.b.a	$126$	$3$	126.b	3.b	$2$	$4$	$4$	$3.433$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		✓	✓	✓	126.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)