Space of modular forms of level 144, weight 2, and trivial character

• Label: 144.2.a
• Level: $144$
• Weight: $2$
• Character orbit: 144.a
• Rep. character: $\chi_{144}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(144))\).

	Total	New	Old
Modular forms	36	3	33
Cusp forms	13	2	11
Eisenstein series	23	1	22

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(8\)	\(0\)	\(8\)		\(3\)	\(0\)	\(3\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(10\)	\(1\)	\(9\)		\(4\)	\(1\)	\(3\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(10\)	\(1\)	\(9\)		\(4\)	\(1\)	\(3\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(8\)	\(1\)	\(7\)		\(2\)	\(0\)	\(2\)		\(6\)	\(1\)	\(5\)
Plus space		\(+\)		\(16\)	\(1\)	\(15\)		\(5\)	\(0\)	\(5\)		\(11\)	\(1\)	\(10\)
Minus space		\(-\)		\(20\)	\(2\)	\(18\)		\(8\)	\(2\)	\(6\)		\(12\)	\(0\)	\(12\)

Trace form

2 * q + 2 * q^5 + 4 * q^7 + 4 * q^11 - 2 * q^17 - 4 * q^19 - 8 * q^23 - 6 * q^25 - 6 * q^29 - 4 * q^31 - 4 * q^37 + 6 * q^41 - 12 * q^43 + 2 * q^49 + 2 * q^53 + 8 * q^55 + 4 * q^59 + 12 * q^61 - 4 * q^65 + 20 * q^67 + 8 * q^71 + 12 * q^79 - 4 * q^83 - 4 * q^85 + 6 * q^89 + 8 * q^91 + 8 * q^95 + 16 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(144))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
144.2.a.a	$144$	$2$	144.a	1.a	$1$	$1$	$1$	$1.150$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓		✓	✓	36.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{7}+2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
144.2.a.b	$144$	$2$	144.a	1.a	$1$	$1$	$1$	$1.150$	\(\Q\)	None	✓		✓	✓	24.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(144)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)