Space of modular forms of level 192, weight 14, and trivial character

• Label: 192.14.a
• Level: $192$
• Weight: $14$
• Character orbit: 192.a
• Rep. character: $\chi_{192}(1,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $26$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	192.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(192))\).

	Total	New	Old
Modular forms	428	52	376
Cusp forms	404	52	352
Eisenstein series	24	0	24

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
\(+\)	\(+\)	\(+\)		\(106\)	\(13\)	\(93\)		\(100\)	\(13\)	\(87\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)		\(108\)	\(14\)	\(94\)		\(102\)	\(14\)	\(88\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(108\)	\(13\)	\(95\)		\(102\)	\(13\)	\(89\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(106\)	\(12\)	\(94\)		\(100\)	\(12\)	\(88\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(212\)	\(25\)	\(187\)		\(200\)	\(25\)	\(175\)		\(12\)	\(0\)	\(12\)
Minus space		\(-\)		\(216\)	\(27\)	\(189\)		\(204\)	\(27\)	\(177\)		\(12\)	\(0\)	\(12\)

Trace form

52 * q + 27634932 * q^9 - 35040088 * q^13 + 198858392 * q^17 - 897958872 * q^21 + 13890416012 * q^25 + 7323327664 * q^29 - 7023039272 * q^37 - 36966257128 * q^41 + 719746934452 * q^49 + 446039586736 * q^53 - 201240887720 * q^61 - 573950108160 * q^65 - 168688465488 * q^69 - 62518379032 * q^73 - 3817482686816 * q^77 + 14686335897012 * q^81 - 10334757542752 * q^85 + 2617033184488 * q^89 - 14379567334488 * q^93 + 8990431223496 * q^97

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(192))\) 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
192.14.a.a	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				6.14.a.a	$1$	$0$	\(0\)	\(-729\)	\(-54654\)	\(-176336\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}-54654q^{5}-176336q^{7}+\cdots\)
192.14.a.b	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				12.14.a.a	$1$	$0$	\(0\)	\(-729\)	\(14850\)	\(62896\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+14850q^{5}+62896q^{7}+\cdots\)
192.14.a.c	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				24.14.a.a	$1$	$1$	\(0\)	\(-729\)	\(22490\)	\(181272\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+22490q^{5}+181272q^{7}+\cdots\)
192.14.a.d	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				12.14.a.b	$1$	$1$	\(0\)	\(-729\)	\(24570\)	\(-173704\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+24570q^{5}-173704q^{7}+\cdots\)
192.14.a.e	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				3.14.a.a	$1$	$0$	\(0\)	\(-729\)	\(30210\)	\(-235088\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+30210q^{5}-235088q^{7}+\cdots\)
192.14.a.f	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				6.14.a.a	$1$	$0$	\(0\)	\(729\)	\(-54654\)	\(176336\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}-54654q^{5}+176336q^{7}+\cdots\)
192.14.a.g	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				12.14.a.a	$1$	$0$	\(0\)	\(729\)	\(14850\)	\(-62896\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+14850q^{5}-62896q^{7}+\cdots\)
192.14.a.h	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				24.14.a.a	$1$	$1$	\(0\)	\(729\)	\(22490\)	\(-181272\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+22490q^{5}-181272q^{7}+\cdots\)
192.14.a.i	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				12.14.a.b	$1$	$1$	\(0\)	\(729\)	\(24570\)	\(173704\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+24570q^{5}+173704q^{7}+\cdots\)
192.14.a.j	$192$	$14$	192.a	1.a	$1$	$1$	$1$	$205.883$	\(\Q\)	None	✓				3.14.a.a	$1$	$0$	\(0\)	\(729\)	\(30210\)	\(235088\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+30210q^{5}+235088q^{7}+\cdots\)
192.14.a.k	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{1969}) \)	None	✓				3.14.a.b	$1$	$1$	\(0\)	\(-1458\)	\(-40716\)	\(-21008\)		$+$	$+$	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(-20358-\beta )q^{5}+(-10504+\cdots)q^{7}+\cdots\)
192.14.a.l	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{62869}) \)	None	✓				24.14.a.d	$1$	$1$	\(0\)	\(-1458\)	\(-5068\)	\(104880\)		$+$	$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(-2534-\beta )q^{5}+(52440+\cdots)q^{7}+\cdots\)
192.14.a.m	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{1621}) \)	None	✓				24.14.a.c	$1$	$0$	\(0\)	\(-1458\)	\(11204\)	\(-275808\)		$-$	$+$	$-$	$2^{9}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(5602-\beta )q^{5}+(-137904+\cdots)q^{7}+\cdots\)
192.14.a.n	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{406}) \)	None	✓				24.14.a.b	$1$	$0$	\(0\)	\(-1458\)	\(30916\)	\(532896\)		$-$	$+$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(15458+7\beta )q^{5}+(266448+\cdots)q^{7}+\cdots\)
192.14.a.o	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{1969}) \)	None	✓				3.14.a.b	$1$	$1$	\(0\)	\(1458\)	\(-40716\)	\(21008\)		$-$	$-$	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(-20358-\beta )q^{5}+(10504+\cdots)q^{7}+\cdots\)
192.14.a.p	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{62869}) \)	None	✓				24.14.a.d	$1$	$1$	\(0\)	\(1458\)	\(-5068\)	\(-104880\)		$-$	$-$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(-2534-\beta )q^{5}+(-52440+\cdots)q^{7}+\cdots\)
192.14.a.q	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{1621}) \)	None	✓				24.14.a.c	$1$	$0$	\(0\)	\(1458\)	\(11204\)	\(275808\)		$+$	$-$	$-$	$2^{9}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(5602-\beta )q^{5}+(137904+\cdots)q^{7}+\cdots\)
192.14.a.r	$192$	$14$	192.a	1.a	$1$	$2$	$2$	$205.883$	\(\Q(\sqrt{406}) \)	None	✓				24.14.a.b	$1$	$0$	\(0\)	\(1458\)	\(30916\)	\(-532896\)		$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(15458+7\beta )q^{5}+(-266448+\cdots)q^{7}+\cdots\)
192.14.a.s	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.c	$1$	$0$	\(0\)	\(-2187\)	\(-45966\)	\(684108\)		$-$	$+$	$-$	$2^{14}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(-15322+\beta _{1})q^{5}+(228036+\cdots)q^{7}+\cdots\)
192.14.a.t	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.b	$1$	$1$	\(0\)	\(-2187\)	\(11594\)	\(175316\)		$+$	$+$	$+$	$2^{15}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(3865+\beta _{1})q^{5}+(58438+\cdots)q^{7}+\cdots\)
192.14.a.u	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.a	$1$	$0$	\(0\)	\(-2187\)	\(20226\)	\(-140868\)		$-$	$+$	$-$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(6742-\beta _{1}+2\beta _{2})q^{5}+(-46956+\cdots)q^{7}+\cdots\)
192.14.a.v	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.c	$1$	$1$	\(0\)	\(2187\)	\(-45966\)	\(-684108\)		$-$	$-$	$+$	$2^{14}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(-15322+\beta _{1})q^{5}+(-228036+\cdots)q^{7}+\cdots\)
192.14.a.w	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.b	$1$	$0$	\(0\)	\(2187\)	\(11594\)	\(-175316\)		$+$	$-$	$-$	$2^{15}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(3865+\beta _{1})q^{5}+(-58438+\cdots)q^{7}+\cdots\)
192.14.a.x	$192$	$14$	192.a	1.a	$1$	$3$	$3$	$205.883$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				96.14.a.a	$1$	$1$	\(0\)	\(2187\)	\(20226\)	\(140868\)		$-$	$-$	$+$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(6742-\beta _{1}+2\beta _{2})q^{5}+(46956+\cdots)q^{7}+\cdots\)
192.14.a.y	$192$	$14$	192.a	1.a	$1$	$4$	$4$	$205.883$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		96.14.a.g	$1$	$1$	\(0\)	\(-2916\)	\(-19656\)	\(-102672\)		$+$	$+$	$+$	$2^{27}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}+(-4914-\beta _{1})q^{5}+(-25668+\cdots)q^{7}+\cdots\)
192.14.a.z	$192$	$14$	192.a	1.a	$1$	$4$	$4$	$205.883$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		96.14.a.g	$1$	$0$	\(0\)	\(2916\)	\(-19656\)	\(102672\)		$+$	$-$	$-$	$2^{27}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}+(-4914-\beta _{1})q^{5}+(25668+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(192)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)