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

• Label: 126.7.s
• Level: $126$
• Weight: $7$
• Character orbit: 126.s
• Rep. character: $\chi_{126}(53,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	304	32	272
Cusp forms	272	32	240
Eisenstein series	32	0	32

Trace form

32 * q + 512 * q^4 + 1448 * q^7 - 1344 * q^10 + 12880 * q^13 - 16384 * q^16 + 10528 * q^19 - 41088 * q^22 + 21080 * q^25 - 7936 * q^28 + 92008 * q^31 + 94080 * q^34 - 112856 * q^37 + 43008 * q^40 - 795296 * q^43 + 47040 * q^46 + 513104 * q^49 + 206080 * q^52 - 19824 * q^55 - 184704 * q^58 - 463568 * q^61 - 1048576 * q^64 - 845072 * q^67 - 839040 * q^70 + 375928 * q^73 + 673792 * q^76 + 2499784 * q^79 - 1696128 * q^82 + 898464 * q^85 - 657408 * q^88 - 887216 * q^91 + 489216 * q^94 + 12743248 * q^97

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.s.a	$126$	$7$	126.s	21.h	$6$	$16$	$8$	$28.987$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			126.7.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(552\)	$2^{12}\cdot 3^{6}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+4\beta _{2}q^{2}-2^{5}\beta _{1}q^{4}+(4\beta _{2}-\beta _{4})q^{5}+\cdots\)
126.7.s.b	$126$	$7$	126.s	21.h	$6$	$16$	$8$	$28.987$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			126.7.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(896\)	$2^{16}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(4\beta _{2}-4\beta _{3})q^{2}-2^{5}\beta _{1}q^{4}+(-5^{2}\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{7}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)