Space of modular forms of level 144, weight 8, and trivial character

• Label: 144.8.a
• Level: $144$
• Weight: $8$
• Character orbit: 144.a
• Rep. character: $\chi_{144}(1,\cdot)$
• Character field: $\Q$
• Dimension: $17$
• Newform subspaces: $14$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	144.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(144))\).

	Total	New	Old
Modular forms	180	18	162
Cusp forms	156	17	139
Eisenstein series	24	1	23

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
\(+\)	\(+\)	\(+\)		\(46\)	\(4\)	\(42\)		\(40\)	\(4\)	\(36\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)		\(44\)	\(5\)	\(39\)		\(38\)	\(5\)	\(33\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(44\)	\(3\)	\(41\)		\(38\)	\(3\)	\(35\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(46\)	\(6\)	\(40\)		\(40\)	\(5\)	\(35\)		\(6\)	\(1\)	\(5\)
Plus space		\(+\)		\(92\)	\(10\)	\(82\)		\(80\)	\(9\)	\(71\)		\(12\)	\(1\)	\(11\)
Minus space		\(-\)		\(88\)	\(8\)	\(80\)		\(76\)	\(8\)	\(68\)		\(12\)	\(0\)	\(12\)

Trace form

17 * q + 140 * q^5 - 1348 * q^7 - 3392 * q^11 - 3278 * q^13 + 11260 * q^17 - 136 * q^19 - 78992 * q^23 + 240587 * q^25 - 7956 * q^29 - 62884 * q^31 + 31536 * q^35 - 228482 * q^37 + 133452 * q^41 - 94408 * q^43 - 23184 * q^47 + 2420169 * q^49 + 615164 * q^53 + 672672 * q^55 - 526736 * q^59 - 271802 * q^61 - 834328 * q^65 + 5292224 * q^67 + 2617712 * q^71 - 188498 * q^73 + 1831008 * q^77 + 656060 * q^79 - 4232800 * q^83 + 9182472 * q^85 - 10976772 * q^89 + 21664888 * q^91 + 10625120 * q^95 + 392278 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(144))\) 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
144.8.a.a	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				8.8.a.b	$1$	$1$	\(0\)	\(0\)	\(-430\)	\(1224\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-430q^{5}+1224q^{7}-3164q^{11}+\cdots\)
144.8.a.b	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				3.8.a.a	$1$	$0$	\(0\)	\(0\)	\(-390\)	\(64\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-390q^{5}+2^{6}q^{7}-948q^{11}-5098q^{13}+\cdots\)
144.8.a.c	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				12.8.a.b	$1$	$0$	\(0\)	\(0\)	\(-270\)	\(-1112\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-270q^{5}-1112q^{7}-5724q^{11}+\cdots\)
144.8.a.d	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				24.8.a.c	$1$	$1$	\(0\)	\(0\)	\(-110\)	\(-504\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-110q^{5}-504q^{7}+3812q^{11}+9574q^{13}+\cdots\)
144.8.a.e	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				36.8.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(508\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+508q^{7}-14614q^{13}+57448q^{19}+\cdots\)
144.8.a.f	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				24.8.a.a	$1$	$1$	\(0\)	\(0\)	\(26\)	\(-1056\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+26q^{5}-1056q^{7}+6412q^{11}+5206q^{13}+\cdots\)
144.8.a.g	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				8.8.a.a	$1$	$1$	\(0\)	\(0\)	\(82\)	\(456\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+82q^{5}+456q^{7}-2524q^{11}-10778q^{13}+\cdots\)
144.8.a.h	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				6.8.a.a	$1$	$0$	\(0\)	\(0\)	\(114\)	\(1576\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+114q^{5}+1576q^{7}+7332q^{11}+\cdots\)
144.8.a.i	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				2.8.a.a	$1$	$0$	\(0\)	\(0\)	\(210\)	\(-1016\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+210q^{5}-1016q^{7}+1092q^{11}+\cdots\)
144.8.a.j	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				12.8.a.a	$1$	$0$	\(0\)	\(0\)	\(378\)	\(832\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+378q^{5}+832q^{7}-2484q^{11}+14870q^{13}+\cdots\)
144.8.a.k	$144$	$8$	144.a	1.a	$1$	$1$	$1$	$44.983$	\(\Q\)	None	✓				24.8.a.b	$1$	$1$	\(0\)	\(0\)	\(530\)	\(-120\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+530q^{5}-120q^{7}-7196q^{11}-9626q^{13}+\cdots\)
144.8.a.l	$144$	$8$	144.a	1.a	$1$	$2$	$2$	$44.983$	\(\Q(\sqrt{46}) \)	None	✓				72.8.a.f	$1$	$0$	\(0\)	\(0\)	\(-224\)	\(-840\)		$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-112+\beta )q^{5}+(-420+4\beta )q^{7}+\cdots\)
144.8.a.m	$144$	$8$	144.a	1.a	$1$	$2$	$2$	$44.983$	\(\Q(\sqrt{10}) \)	None	✓		✓		9.8.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-520\)		$-$	$+$	$-$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-260q^{7}-20\beta q^{11}+6890q^{13}+\cdots\)
144.8.a.n	$144$	$8$	144.a	1.a	$1$	$2$	$2$	$44.983$	\(\Q(\sqrt{46}) \)	None	✓				72.8.a.f	$1$	$0$	\(0\)	\(0\)	\(224\)	\(-840\)		$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(112+\beta )q^{5}+(-420-4\beta )q^{7}+(320+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(144)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)