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

• Label: 144.2.i
• Level: $144$
• Weight: $2$
• Character orbit: 144.i
• Rep. character: $\chi_{144}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	60	14	46
Cusp forms	36	10	26
Eisenstein series	24	4	20

Trace form

10 * q + 2 * q^3 - q^5 + q^7 - 4 * q^9 + 7 * q^11 - q^13 + 5 * q^15 - 8 * q^17 + 4 * q^19 - 3 * q^21 - 5 * q^23 - 2 * q^25 - 16 * q^27 + 3 * q^29 + 7 * q^31 - 5 * q^33 - 30 * q^35 - 4 * q^37 - 31 * q^39 - 3 * q^41 + 7 * q^43 + 11 * q^45 - 15 * q^47 + 10 * q^51 - 4 * q^53 - 6 * q^55 - 10 * q^57 + 25 * q^59 - q^61 + 33 * q^63 + 17 * q^65 + q^67 + 13 * q^69 + 56 * q^71 - 16 * q^73 + 46 * q^75 + 21 * q^77 + q^79 + 20 * q^81 + 29 * q^83 - 6 * q^85 + 15 * q^87 + 12 * q^89 - 22 * q^91 + 5 * q^93 - 28 * q^95 + 5 * q^97 - 47 * 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.i.a	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
144.2.i.b	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None					72.2.i.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
144.2.i.c	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
144.2.i.d	$144$	$2$	144.i	9.c	$3$	$4$	$2$	$1.150$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None			✓		72.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)