Space of modular forms of level 126, weight 7, and Character 126.j

• Label: 126.7.j
• Level: $126$
• Weight: $7$
• Character orbit: 126.j
• Rep. character: $\chi_{126}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	126.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(126, [\chi])\).

	Total	New	Old
Modular forms	296	96	200
Cusp forms	280	96	184
Eisenstein series	16	0	16

Trace form

96 * q - 1536 * q^4 - 240 * q^7 - 216 * q^9 + 1152 * q^11 + 5040 * q^13 + 1584 * q^14 - 480 * q^15 - 49152 * q^16 + 18144 * q^17 - 3168 * q^18 - 8424 * q^21 + 9648 * q^23 - 10752 * q^24 - 300000 * q^25 + 30240 * q^26 + 73836 * q^27 - 7680 * q^28 + 26748 * q^29 - 109440 * q^30 - 27720 * q^31 - 10080 * q^33 + 39384 * q^35 - 66048 * q^36 - 18480 * q^37 + 109536 * q^39 - 388584 * q^41 + 68256 * q^42 + 21840 * q^43 - 18432 * q^44 + 326172 * q^45 + 67536 * q^46 + 124740 * q^47 - 138864 * q^49 - 49536 * q^50 - 228108 * q^51 + 300240 * q^53 + 141120 * q^54 - 101376 * q^56 - 456888 * q^57 + 318528 * q^58 - 756000 * q^59 + 22272 * q^60 + 510048 * q^61 - 1897236 * q^63 + 3145728 * q^64 - 260136 * q^65 + 73920 * q^66 + 517440 * q^67 - 1681680 * q^69 + 155952 * q^70 - 601632 * q^71 - 218112 * q^72 - 786240 * q^74 - 2052960 * q^75 + 1845000 * q^77 + 893568 * q^78 + 419556 * q^79 - 256788 * q^81 - 254016 * q^83 + 563328 * q^84 - 828000 * q^85 + 3327552 * q^86 - 2823240 * q^87 - 3011148 * q^89 + 977760 * q^90 + 792000 * q^91 - 154368 * q^92 + 156720 * q^93 - 2750472 * q^95 + 344064 * q^96 + 2106720 * q^97 + 1989504 * q^98 - 870912 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(126, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.7.j.a	$126$	$7$	126.j	63.k	$6$	$96$	$48$	$28.987$		None		✓	✓	✓	126.7.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-240\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{7}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)