Space of modular forms of level 138, weight 2, and Character 138.d

• Label: 138.2.d
• Level: $138$
• Weight: $2$
• Character orbit: 138.d
• Rep. character: $\chi_{138}(137,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(138, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	20	8	12
Eisenstein series	8	0	8

Trace form

8 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 + 4 * q^12 - 8 * q^13 + 8 * q^16 - 16 * q^18 + 4 * q^24 + 48 * q^25 - 28 * q^27 + 16 * q^31 + 24 * q^39 + 16 * q^46 - 4 * q^48 - 56 * q^49 + 8 * q^52 + 28 * q^54 - 64 * q^55 + 8 * q^58 - 8 * q^64 + 28 * q^69 - 24 * q^70 + 16 * q^72 - 8 * q^73 - 4 * q^75 - 16 * q^78 + 8 * q^81 + 24 * q^85 - 56 * q^87 - 8 * q^93 + 56 * q^94 - 4 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(138, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
138.2.d.a	$138$	$2$	138.d	69.c	$2$	$8$	$8$	$1.102$	8.0.\(\cdots\).3	None		✓	✓	✓	138.2.d.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

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