Space of modular forms of level 126, weight 2, and Character 126.k

• Label: 126.2.k
• Level: $126$
• Weight: $2$
• Character orbit: 126.k
• Rep. character: $\chi_{126}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).

	Total	New	Old
Modular forms	64	8	56
Cusp forms	32	8	24
Eisenstein series	32	0	32

Trace form

8 * q + 4 * q^4 + 4 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 - 24 * q^22 - 16 * q^25 - 4 * q^28 - 12 * q^31 - 16 * q^37 + 12 * q^40 + 32 * q^43 + 20 * q^49 + 12 * q^58 + 24 * q^61 - 8 * q^64 + 40 * q^67 - 12 * q^70 + 24 * q^73 + 28 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 - 24 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.2.k.a	$126$	$2$	126.k	21.g	$6$	$8$	$4$	$1.006$	\(\Q(\zeta_{24})\)	None		✓	✓	✓	126.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta_{3}+\beta_1)q^{2}+(-\beta_{2}+1)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

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