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

• Label: 126.7.q
• Level: $126$
• Weight: $7$
• Character orbit: 126.q
• Rep. character: $\chi_{126}(29,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• 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.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
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	72	224
Cusp forms	280	72	208
Eisenstein series	16	0	16

Trace form

72 * q + 84 * q^3 + 1152 * q^4 - 864 * q^5 - 160 * q^6 - 1484 * q^9 + 972 * q^11 - 768 * q^12 + 3136 * q^15 - 36864 * q^16 + 15936 * q^18 + 19080 * q^19 - 27648 * q^20 - 10976 * q^21 + 7200 * q^22 + 30888 * q^23 + 5120 * q^24 + 133812 * q^25 - 145656 * q^27 - 168480 * q^29 - 25376 * q^30 - 24480 * q^31 + 225956 * q^33 + 54720 * q^34 + 29056 * q^36 + 124992 * q^37 - 195264 * q^38 - 116840 * q^39 + 509652 * q^41 - 99180 * q^43 - 494584 * q^45 - 944784 * q^47 - 110592 * q^48 - 605052 * q^49 - 81216 * q^50 + 34196 * q^51 + 805568 * q^54 - 766656 * q^55 + 385452 * q^57 - 2251476 * q^59 - 119552 * q^60 + 57624 * q^63 - 2359296 * q^64 + 2936520 * q^65 - 62272 * q^66 - 455004 * q^67 - 328320 * q^68 - 1440232 * q^69 + 313344 * q^72 + 356040 * q^73 + 2035584 * q^74 + 1415116 * q^75 + 305280 * q^76 + 1524224 * q^78 + 220896 * q^79 + 2245660 * q^81 - 2146176 * q^82 - 793800 * q^83 - 702464 * q^84 - 2411136 * q^85 - 4930848 * q^86 - 978320 * q^87 - 230400 * q^88 + 3761600 * q^90 - 1580544 * q^91 + 988416 * q^92 + 6329776 * q^93 + 3745224 * q^95 + 327680 * q^96 + 1482228 * q^97 - 715592 * 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.q.a	$126$	$7$	126.q	9.d	$6$	$72$	$36$	$28.987$		None		✓	✓	✓	126.7.q.a	$2$	$0$	\(0\)	\(84\)	\(-864\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{7}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)