Space of modular forms of level 144, weight 14, and trivial character

• Label: 144.14.a
• Level: $144$
• Weight: $14$
• Character orbit: 144.a
• Rep. character: $\chi_{144}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $21$
• Sturm bound: $336$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	144.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(336\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(144))\).

	Total	New	Old
Modular forms	324	33	291
Cusp forms	300	32	268
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	Dim
\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(9\)
Plus space		\(+\)	\(15\)
Minus space		\(-\)	\(17\)

Trace form

32 * q + 16902 * q^5 + 170068 * q^7 + 2952684 * q^11 + 8510580 * q^13 + 52444602 * q^17 - 547588252 * q^19 - 678198456 * q^23 + 8336604204 * q^25 - 219214674 * q^29 + 5197237628 * q^31 + 21729468384 * q^35 - 12181051216 * q^37 - 2558333646 * q^41 + 10257973068 * q^43 + 15344864352 * q^47 + 486318581360 * q^49 + 54937343142 * q^53 - 587406016936 * q^55 - 402535353780 * q^59 - 13177074672 * q^61 - 493806381228 * q^65 + 782693463068 * q^67 - 1045304331912 * q^71 - 1172190446340 * q^73 - 790348739904 * q^77 + 1166028593772 * q^79 + 1182440308500 * q^83 + 1561774631348 * q^85 - 231398888238 * q^89 + 1271398615592 * q^91 + 3975180336216 * q^95 + 1675561670428 * q^97

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(144))\) 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
144.14.a.a	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				4.14.a.a	$1$	$1$	\(0\)	\(0\)	\(-56214\)	\(-333032\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-56214q^{5}-333032q^{7}-6397380q^{11}+\cdots\)
144.14.a.b	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				6.14.a.a	$1$	$1$	\(0\)	\(0\)	\(-54654\)	\(-176336\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-54654q^{5}-176336q^{7}+6612420q^{11}+\cdots\)
144.14.a.c	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				18.14.a.b	$1$	$0$	\(0\)	\(0\)	\(-15936\)	\(-98252\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-15936q^{5}-98252q^{7}-1630464q^{11}+\cdots\)
144.14.a.d	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				2.14.a.a	$1$	$1$	\(0\)	\(0\)	\(-3990\)	\(433432\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3990q^{5}+433432q^{7}+1619772q^{11}+\cdots\)
144.14.a.e	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				36.14.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-615884\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-615884q^{7}-17048302q^{13}-231547688q^{19}+\cdots\)
144.14.a.f	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				8.14.a.a	$1$	$0$	\(0\)	\(0\)	\(4330\)	\(139992\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4330q^{5}+139992q^{7}-6484324q^{11}+\cdots\)
144.14.a.g	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				12.14.a.a	$1$	$1$	\(0\)	\(0\)	\(14850\)	\(62896\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+14850q^{5}+62896q^{7}+5104836q^{11}+\cdots\)
144.14.a.h	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				18.14.a.b	$1$	$0$	\(0\)	\(0\)	\(15936\)	\(-98252\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+15936q^{5}-98252q^{7}+1630464q^{11}+\cdots\)
144.14.a.i	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				24.14.a.a	$1$	$0$	\(0\)	\(0\)	\(22490\)	\(-181272\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+22490q^{5}-181272q^{7}-9261428q^{11}+\cdots\)
144.14.a.j	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				12.14.a.b	$1$	$1$	\(0\)	\(0\)	\(24570\)	\(173704\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+24570q^{5}+173704q^{7}-970164q^{11}+\cdots\)
144.14.a.k	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				3.14.a.a	$1$	$1$	\(0\)	\(0\)	\(30210\)	\(-235088\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+30210q^{5}-235088q^{7}-11182908q^{11}+\cdots\)
144.14.a.l	$144$	$14$	144.a	1.a	$1$	$1$	$1$	$154.413$	\(\Q\)	None	✓				2.14.a.b	$1$	$1$	\(0\)	\(0\)	\(57450\)	\(-64232\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+57450q^{5}-64232q^{7}+2464572q^{11}+\cdots\)
144.14.a.m	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{1969}) \)	None	✓		✓		3.14.a.b	$1$	$1$	\(0\)	\(0\)	\(-40716\)	\(21008\)		$-$	$-$	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-20358-\beta )q^{5}+(10504+3^{3}\beta )q^{7}+\cdots\)
144.14.a.n	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{781}) \)	None	✓				8.14.a.b	$1$	$0$	\(0\)	\(0\)	\(-18476\)	\(-110928\)		$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-9238-4\beta )q^{5}+(-55464+74\beta )q^{7}+\cdots\)
144.14.a.o	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{62869}) \)	None	✓				24.14.a.d	$1$	$0$	\(0\)	\(0\)	\(-5068\)	\(-104880\)		$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2534-\beta )q^{5}+(-52440-5\beta )q^{7}+\cdots\)
144.14.a.p	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{55}) \)	None	✓				9.14.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(266600\)		$-$	$+$	$-$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q+65\beta q^{5}+133300q^{7}+11300\beta q^{11}+\cdots\)
144.14.a.q	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{3535}) \)	None	✓				36.14.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(862568\)		$-$	$+$	$-$	$2^{5}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+431284q^{7}-220\beta q^{11}+\cdots\)
144.14.a.r	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{1621}) \)	None	✓				24.14.a.c	$1$	$0$	\(0\)	\(0\)	\(11204\)	\(-275808\)		$+$	$-$	$-$	$2^{9}\cdot 3$	$\mathrm{SU}(2)$	\(q+(5602-\beta )q^{5}+(-137904+13\beta )q^{7}+\cdots\)
144.14.a.s	$144$	$14$	144.a	1.a	$1$	$2$	$2$	$154.413$	\(\Q(\sqrt{406}) \)	None	✓				24.14.a.b	$1$	$0$	\(0\)	\(0\)	\(30916\)	\(532896\)		$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(15458+7\beta )q^{5}+(266448+37\beta )q^{7}+\cdots\)
144.14.a.t	$144$	$14$	144.a	1.a	$1$	$3$	$3$	$154.413$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				72.14.a.g	$1$	$1$	\(0\)	\(0\)	\(-50256\)	\(-14532\)		$+$	$+$	$+$	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-16752+\beta _{2})q^{5}+(-4844+\beta _{1}+\cdots)q^{7}+\cdots\)
144.14.a.u	$144$	$14$	144.a	1.a	$1$	$3$	$3$	$154.413$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				72.14.a.g	$1$	$1$	\(0\)	\(0\)	\(50256\)	\(-14532\)		$+$	$+$	$+$	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(16752-\beta _{2})q^{5}+(-4844+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(144)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)