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

• Label: 138.2.e
• Level: $138$
• Weight: $2$
• Character orbit: 138.e
• Rep. character: $\chi_{138}(13,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	280	40	240
Cusp forms	200	40	160
Eisenstein series	80	0	80

Trace form

40 * q - 4 * q^4 + 8 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^10 + 24 * q^11 + 16 * q^13 + 8 * q^14 + 8 * q^15 - 4 * q^16 - 20 * q^17 - 16 * q^19 - 36 * q^20 + 4 * q^21 - 32 * q^22 - 64 * q^23 - 52 * q^25 - 28 * q^26 - 36 * q^28 - 12 * q^29 + 12 * q^30 - 12 * q^31 + 12 * q^33 + 24 * q^34 + 20 * q^35 - 4 * q^36 - 16 * q^37 + 32 * q^38 - 36 * q^39 + 4 * q^40 - 12 * q^41 + 12 * q^42 + 16 * q^43 + 24 * q^44 + 8 * q^45 + 20 * q^46 - 48 * q^47 + 44 * q^49 + 24 * q^50 - 16 * q^51 + 16 * q^52 - 12 * q^53 - 24 * q^55 + 8 * q^56 - 32 * q^57 - 12 * q^58 + 20 * q^59 + 8 * q^60 - 28 * q^61 + 40 * q^62 + 8 * q^63 - 4 * q^64 + 64 * q^65 + 24 * q^66 + 8 * q^67 + 24 * q^68 + 20 * q^69 - 16 * q^70 + 72 * q^71 + 44 * q^73 + 8 * q^74 + 32 * q^75 + 28 * q^76 + 64 * q^77 + 16 * q^78 - 44 * q^79 + 8 * q^80 - 4 * q^81 - 4 * q^82 + 20 * q^83 + 4 * q^84 + 8 * q^85 + 40 * q^86 + 40 * q^87 + 12 * q^88 + 28 * q^89 + 4 * q^90 + 56 * q^91 + 24 * q^92 + 32 * q^93 + 24 * q^94 - 28 * q^95 + 68 * q^97 - 56 * q^98 - 20 * q^99

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.e.a	$138$	$2$	138.e	23.c	$11$	$10$	$1$	$1.102$	\(\Q(\zeta_{22})\)	None		✓			138.2.e.a	$2$	$0$	\(-1\)	\(-1\)	\(8\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.b	$138$	$2$	138.e	23.c	$11$	$10$	$1$	$1.102$	\(\Q(\zeta_{22})\)	None		✓			138.2.e.b	$2$	$0$	\(-1\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
138.2.e.c	$138$	$2$	138.e	23.c	$11$	$10$	$1$	$1.102$	\(\Q(\zeta_{22})\)	None		✓			138.2.e.c	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.d	$138$	$2$	138.e	23.c	$11$	$10$	$1$	$1.102$	\(\Q(\zeta_{22})\)	None		✓			138.2.e.d	$2$	$0$	\(1\)	\(1\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)

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

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