Space of modular forms of level 138, weight 4, and Character 138.d

• Label: 138.4.d
• Level: $138$
• Weight: $4$
• Character orbit: 138.d
• Rep. character: $\chi_{138}(137,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(138, [\chi])\).

	Total	New	Old
Modular forms	76	24	52
Cusp forms	68	24	44
Eisenstein series	8	0	8

Trace form

24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(138, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
138.4.d.a	$138$	$4$	138.d	69.c	$2$	$24$	$24$	$8.142$		None		✓	✓	✓	138.4.d.a	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(138, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)