Space of modular forms of level 126, weight 3, and Character 126.c

• Label: 126.3.c
• Level: $126$
• Weight: $3$
• Character orbit: 126.c
• Rep. character: $\chi_{126}(55,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$126 = 2 \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	126.c (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$7$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$72$
Trace bound:			$7$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(126, [\chi])$.

	Total	New	Old
Modular forms	56	8	48
Cusp forms	40	8	32
Eisenstein series	16	0	16

Trace form

8 * q + 16 * q^4 - 8 * q^7 + 24 * q^11 + 24 * q^14 + 32 * q^16 + 48 * q^22 - 24 * q^23 - 136 * q^25 - 16 * q^28 - 120 * q^29 + 24 * q^35 - 16 * q^37 + 80 * q^43 + 48 * q^44 + 48 * q^46 - 88 * q^49 - 96 * q^50 + 216 * q^53 + 48 * q^56 - 192 * q^58 + 64 * q^64 - 240 * q^65 - 32 * q^67 - 192 * q^70 + 120 * q^71 - 288 * q^74 - 24 * q^77 + 544 * q^79 - 48 * q^85 + 240 * q^86 + 96 * q^88 + 528 * q^91 - 48 * q^92 + 240 * q^95 + 192 * q^98

Decomposition of $S_{3}^{\mathrm{new}}(126, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.3.c.a	$126$	$3$	126.c	7.b	$2$	$4$	$4$	$3.433$	$\Q(\sqrt{2}, \sqrt{-33})$	None		✓			126.3.c.a	$4$	$0$	$0$	$0$	$0$	$-16$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+2q^{4}-\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+\cdots$
126.3.c.b	$126$	$3$	126.c	7.b	$2$	$4$	$4$	$3.433$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.c.a	$2$	$0$	$0$	$0$	$0$	$8$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(126, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(126, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(7, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(21, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(42, [\chi])$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(63, [\chi])$$^{\oplus 2}$