Space of modular forms of level 144, weight 2, and Character 144.x

• Label: 144.2.x
• Level: $144$
• Weight: $2$
• Character orbit: 144.x
• Rep. character: $\chi_{144}(13,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

	Total	New	Old
Modular forms	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

88 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - 10 * q^6 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 8 * q^12 - 2 * q^13 - 10 * q^14 - 8 * q^15 - 2 * q^16 - 16 * q^17 - 18 * q^18 - 8 * q^19 + 12 * q^20 - 10 * q^21 - 2 * q^22 - 40 * q^24 - 40 * q^26 + 8 * q^27 - 24 * q^28 - 2 * q^29 + 6 * q^30 - 4 * q^31 - 22 * q^32 - 8 * q^33 - 6 * q^34 - 28 * q^35 + 14 * q^36 - 8 * q^37 + 26 * q^38 - 2 * q^40 - 16 * q^42 - 2 * q^43 + 36 * q^44 - 14 * q^45 + 8 * q^46 - 44 * q^47 + 2 * q^48 + 16 * q^49 - 36 * q^50 - 36 * q^51 - 2 * q^52 - 8 * q^53 + 74 * q^54 + 52 * q^56 - 20 * q^58 + 10 * q^59 + 30 * q^60 - 2 * q^61 + 100 * q^62 - 36 * q^63 - 44 * q^64 - 4 * q^65 + 8 * q^66 - 2 * q^67 + 16 * q^68 - 10 * q^69 + 12 * q^70 + 114 * q^72 + 26 * q^74 + 56 * q^75 + 10 * q^76 - 30 * q^77 + 88 * q^78 - 4 * q^79 + 144 * q^80 - 8 * q^81 - 52 * q^82 - 22 * q^83 - 22 * q^84 - 12 * q^85 + 70 * q^86 - 26 * q^88 + 72 * q^90 - 36 * q^91 - 56 * q^92 - 22 * q^93 + 6 * q^94 + 60 * q^95 + 118 * q^96 - 4 * q^97 + 40 * q^98 + 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.2.x.a	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	None		✓			144.2.x.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.b	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	None		✓			144.2.x.b	$2$	$1$	\(-2\)	\(-6\)	\(-8\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.c	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	None		✓			144.2.x.b	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.d	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	None		✓			144.2.x.a	$2$	$0$	\(2\)	\(0\)	\(2\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.e	$144$	$2$	144.x	144.x	$12$	$72$	$18$	$1.150$		None		✓	✓		144.2.x.e	$4$	$0$	\(4\)	\(2\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$