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}$