Space of modular forms of level 144, weight 10, and trivial character

• Label: 144.10.a
• Level: $144$
• Weight: $10$
• Character orbit: 144.a
• Rep. character: $\chi_{144}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $18$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	144.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(144))\).

	Total	New	Old
Modular forms	228	23	205
Cusp forms	204	22	182
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
\(+\)	\(+\)	\(+\)		\(56\)	\(4\)	\(52\)		\(50\)	\(4\)	\(46\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)		\(58\)	\(7\)	\(51\)		\(52\)	\(7\)	\(45\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(58\)	\(5\)	\(53\)		\(52\)	\(5\)	\(47\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(56\)	\(7\)	\(49\)		\(50\)	\(6\)	\(44\)		\(6\)	\(1\)	\(5\)
Plus space		\(+\)		\(112\)	\(11\)	\(101\)		\(100\)	\(10\)	\(90\)		\(12\)	\(1\)	\(11\)
Minus space		\(-\)		\(116\)	\(12\)	\(104\)		\(104\)	\(12\)	\(92\)		\(12\)	\(0\)	\(12\)

Trace form

22 * q - 358 * q^5 + 3428 * q^7 + 76852 * q^11 - 43080 * q^13 - 70106 * q^17 - 485588 * q^19 - 329384 * q^23 + 7763334 * q^25 - 2153934 * q^29 + 3502588 * q^31 - 13768896 * q^35 + 767668 * q^37 + 726606 * q^41 - 8850876 * q^43 - 28765632 * q^47 + 77974390 * q^49 - 10028710 * q^53 - 29916056 * q^55 + 43449460 * q^59 + 7981092 * q^61 + 233985932 * q^65 + 138184708 * q^67 + 179145512 * q^71 + 486881832 * q^73 + 558512256 * q^77 - 112107444 * q^79 + 373614284 * q^83 + 207459148 * q^85 - 269063922 * q^89 + 274960840 * q^91 + 76595816 * q^95 + 383848472 * q^97

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(144))\) 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
144.10.a.a	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				6.10.a.a	$1$	$1$	\(0\)	\(0\)	\(-2694\)	\(3544\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2694q^{5}+3544q^{7}+29580q^{11}+\cdots\)
144.10.a.b	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				8.10.a.b	$1$	$0$	\(0\)	\(0\)	\(-1510\)	\(-10248\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-1510q^{5}-10248q^{7}+3916q^{11}+\cdots\)
144.10.a.c	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				12.10.a.a	$1$	$1$	\(0\)	\(0\)	\(-990\)	\(-8576\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-990q^{5}-8576q^{7}+70596q^{11}+\cdots\)
144.10.a.d	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				2.10.a.a	$1$	$1$	\(0\)	\(0\)	\(-870\)	\(952\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-870q^{5}+952q^{7}-56148q^{11}+\cdots\)
144.10.a.e	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				24.10.a.a	$1$	$0$	\(0\)	\(0\)	\(-830\)	\(-672\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-830q^{5}-672q^{7}-73468q^{11}+\cdots\)
144.10.a.f	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				24.10.a.c	$1$	$0$	\(0\)	\(0\)	\(-614\)	\(-2184\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-614q^{5}-2184q^{7}+4940q^{11}+\cdots\)
144.10.a.g	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				18.10.a.b	$1$	$0$	\(0\)	\(0\)	\(-384\)	\(-5852\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-384q^{5}-5852q^{7}+90624q^{11}+\cdots\)
144.10.a.h	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				9.10.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12580\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+12580q^{7}+118370q^{13}+976696q^{19}+\cdots\)
144.10.a.i	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				18.10.a.b	$1$	$0$	\(0\)	\(0\)	\(384\)	\(-5852\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+384q^{5}-5852q^{7}-90624q^{11}+\cdots\)
144.10.a.j	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				4.10.a.a	$1$	$1$	\(0\)	\(0\)	\(666\)	\(6328\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+666q^{5}+6328q^{7}-30420q^{11}+\cdots\)
144.10.a.k	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				24.10.a.b	$1$	$0$	\(0\)	\(0\)	\(794\)	\(5880\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+794q^{5}+5880q^{7}-30644q^{11}+\cdots\)
144.10.a.l	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				3.10.a.a	$1$	$1$	\(0\)	\(0\)	\(1314\)	\(4480\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+1314q^{5}+4480q^{7}+1476q^{11}+\cdots\)
144.10.a.m	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				3.10.a.b	$1$	$1$	\(0\)	\(0\)	\(1530\)	\(-9128\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+1530q^{5}-9128q^{7}+21132q^{11}+\cdots\)
144.10.a.n	$144$	$10$	144.a	1.a	$1$	$1$	$1$	$74.165$	\(\Q\)	None	✓				8.10.a.a	$1$	$0$	\(0\)	\(0\)	\(2074\)	\(4344\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2074q^{5}+4344q^{7}+93644q^{11}+\cdots\)
144.10.a.o	$144$	$10$	144.a	1.a	$1$	$2$	$2$	$74.165$	\(\Q(\sqrt{886}) \)	None	✓				72.10.a.f	$1$	$1$	\(0\)	\(0\)	\(-736\)	\(2952\)		$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-368+\beta )q^{5}+(1476-4\beta )q^{7}+\cdots\)
144.10.a.p	$144$	$10$	144.a	1.a	$1$	$2$	$2$	$74.165$	\(\Q(\sqrt{70}) \)	None	✓		✓		36.10.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-952\)		$-$	$+$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-476q^{7}+20\beta q^{11}+60002q^{13}+\cdots\)
144.10.a.q	$144$	$10$	144.a	1.a	$1$	$2$	$2$	$74.165$	\(\Q(\sqrt{886}) \)	None	✓				72.10.a.f	$1$	$1$	\(0\)	\(0\)	\(736\)	\(2952\)		$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(368+\beta )q^{5}+(1476+4\beta )q^{7}+(-3392+\cdots)q^{11}+\cdots\)
144.10.a.r	$144$	$10$	144.a	1.a	$1$	$2$	$2$	$74.165$	\(\Q(\sqrt{109}) \)	None	✓		✓		24.10.a.d	$1$	$0$	\(0\)	\(0\)	\(772\)	\(2880\)		$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(386+\beta )q^{5}+(1440-5\beta )q^{7}+(21124+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

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