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

• Label: 126.7.p
• Level: $126$
• Weight: $7$
• Character orbit: 126.p
• Rep. character: $\chi_{126}(103,\cdot)$
• 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.p (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 + 3072 * q^4 - 240 * q^7 - 2064 * q^9 - 576 * q^11 - 5040 * q^13 + 1584 * q^14 - 480 * q^15 + 98304 * q^16 + 18144 * q^17 + 9984 * q^18 - 20460 * q^21 - 4824 * q^23 + 150000 * q^25 + 30240 * q^26 - 73836 * q^27 - 7680 * q^28 + 26748 * q^29 + 17424 * q^30 + 39384 * q^35 - 66048 * q^36 - 18480 * q^37 + 48300 * q^39 + 388584 * q^41 + 43296 * q^42 + 21840 * q^43 - 18432 * q^44 - 215796 * q^45 + 67536 * q^46 + 172392 * q^49 - 49536 * q^50 + 605208 * q^51 - 161280 * q^52 + 300240 * q^53 + 141120 * q^54 + 50688 * q^56 - 456888 * q^57 - 159264 * q^58 - 15360 * q^60 + 1448436 * q^63 + 3145728 * q^64 + 520272 * q^65 + 873600 * q^66 - 1034880 * q^67 + 580608 * q^68 + 1681680 * q^69 - 438048 * q^70 - 601632 * q^71 + 319488 * q^72 + 393120 * q^74 - 1002288 * q^75 - 2331576 * q^77 + 893568 * q^78 - 839112 * q^79 + 625968 * q^81 + 254016 * q^83 - 654720 * q^84 - 828000 * q^85 - 1663776 * q^86 - 342384 * q^87 - 3011148 * q^89 - 977760 * q^90 + 792000 * q^91 - 154368 * q^92 - 3862536 * q^93 + 5500944 * q^95 - 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.p.a	$126$	$7$	126.p	63.t	$6$	$96$	$48$	$28.987$		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

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