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

• Label: 126.2.f
• Level: $126$
• Weight: $2$
• Character orbit: 126.f
• Rep. character: $\chi_{126}(43,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	56	12	44
Cusp forms	40	12	28
Eisenstein series	16	0	16

Trace form

12 * q + 2 * q^2 + 6 * q^3 - 6 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^11 + 4 * q^14 - 8 * q^15 - 6 * q^16 + 4 * q^17 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 18 * q^25 - 36 * q^27 + 8 * q^29 + 16 * q^30 - 12 * q^31 + 2 * q^32 + 14 * q^33 - 6 * q^34 - 8 * q^35 - 2 * q^36 + 24 * q^37 - 14 * q^38 + 28 * q^39 - 18 * q^41 - 6 * q^43 + 4 * q^44 - 40 * q^45 - 6 * q^48 - 6 * q^49 + 10 * q^50 - 22 * q^51 + 2 * q^54 + 24 * q^55 + 4 * q^56 - 6 * q^57 + 14 * q^59 + 16 * q^60 + 24 * q^62 + 12 * q^63 + 12 * q^64 + 36 * q^65 + 32 * q^66 - 18 * q^67 - 2 * q^68 + 32 * q^69 + 16 * q^71 - 6 * q^72 + 12 * q^73 + 4 * q^74 + 22 * q^75 - 6 * q^76 + 8 * q^77 + 20 * q^78 - 12 * q^79 + 8 * q^80 - 26 * q^81 - 36 * q^82 - 44 * q^83 - 8 * q^84 + 12 * q^85 - 2 * q^86 + 16 * q^87 - 6 * q^88 - 24 * q^89 - 52 * q^90 + 24 * q^91 + 4 * q^92 - 8 * q^93 - 44 * q^95 - 4 * q^96 + 6 * q^97 - 4 * q^98 + 4 * q^99

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.f.a	$126$	$2$	126.f	9.c	$3$	$2$	$1$	$1.006$	\(\Q(\sqrt{-3}) \)	None		✓			126.2.f.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.b	$126$	$2$	126.f	9.c	$3$	$2$	$1$	$1.006$	\(\Q(\sqrt{-3}) \)	None		✓			126.2.f.b	$2$	$0$	\(1\)	\(3\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.c	$126$	$2$	126.f	9.c	$3$	$4$	$2$	$1.006$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			126.2.f.c	$2$	$0$	\(-2\)	\(4\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
126.2.f.d	$126$	$2$	126.f	9.c	$3$	$4$	$2$	$1.006$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			126.2.f.d	$2$	$0$	\(2\)	\(-1\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)

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

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