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

• Label: 138.4.e
• Level: $138$
• Weight: $4$
• Character orbit: 138.e
• Rep. character: $\chi_{138}(13,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	760	120	640
Cusp forms	680	120	560
Eisenstein series	80	0	80

Trace form

120 * q - 48 * q^4 - 32 * q^5 + 16 * q^7 - 108 * q^9 - 40 * q^10 - 24 * q^11 - 128 * q^13 + 16 * q^14 - 48 * q^15 - 192 * q^16 - 160 * q^17 + 468 * q^19 + 576 * q^20 - 84 * q^21 + 736 * q^22 + 1768 * q^23 + 1420 * q^25 + 664 * q^26 - 288 * q^28 - 1008 * q^29 - 72 * q^30 - 2152 * q^31 + 252 * q^33 - 656 * q^34 - 1772 * q^35 - 432 * q^36 - 936 * q^37 - 416 * q^38 + 108 * q^39 - 160 * q^40 + 1308 * q^41 - 216 * q^42 + 2016 * q^43 - 96 * q^44 - 288 * q^45 + 520 * q^46 + 5184 * q^47 - 1276 * q^49 - 48 * q^50 - 336 * q^51 - 512 * q^52 + 1620 * q^53 - 6004 * q^55 + 64 * q^56 - 3360 * q^57 - 1208 * q^58 - 3788 * q^59 - 192 * q^60 + 252 * q^61 - 1072 * q^62 + 144 * q^63 - 768 * q^64 + 128 * q^65 - 144 * q^66 + 2604 * q^67 + 768 * q^68 + 780 * q^69 + 5792 * q^70 - 456 * q^71 + 680 * q^73 + 1456 * q^74 - 1680 * q^75 + 112 * q^76 - 448 * q^77 + 192 * q^78 - 3164 * q^79 - 512 * q^80 - 972 * q^81 - 3752 * q^82 + 4708 * q^83 - 336 * q^84 - 5828 * q^85 + 2576 * q^86 - 1464 * q^87 - 928 * q^88 + 3212 * q^89 - 360 * q^90 + 6232 * q^91 - 672 * q^92 - 240 * q^93 + 720 * q^94 - 4472 * q^95 - 20 * q^97 - 12880 * q^98 - 5760 * q^99

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.e.a	$138$	$4$	138.e	23.c	$11$	$30$	$3$	$8.142$		None		✓			138.4.e.a	$2$	$0$	\(-6\)	\(-9\)	\(-20\)	\(-10\)		$\mathrm{SU}(2)[C_{11}]$
138.4.e.b	$138$	$4$	138.e	23.c	$11$	$30$	$3$	$8.142$		None		✓			138.4.e.b	$2$	$0$	\(-6\)	\(9\)	\(-6\)	\(22\)		$\mathrm{SU}(2)[C_{11}]$
138.4.e.c	$138$	$4$	138.e	23.c	$11$	$30$	$3$	$8.142$		None		✓			138.4.e.c	$2$	$0$	\(6\)	\(-9\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{11}]$
138.4.e.d	$138$	$4$	138.e	23.c	$11$	$30$	$3$	$8.142$		None		✓			138.4.e.d	$2$	$0$	\(6\)	\(9\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{4}^{\mathrm{old}}(138, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)