Space of modular forms of level 6384, weight 2, and trivial character

• Label: 6384.2.a
• Level: $6384$
• Weight: $2$
• Character orbit: 6384.a
• Rep. character: $\chi_{6384}(1,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• Newform subspaces: $58$
• Sturm bound: $2560$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6384.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2560\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6384))\).

	Total	New	Old
Modular forms	1304	108	1196
Cusp forms	1257	108	1149
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(74\)	\(8\)	\(66\)		\(72\)	\(8\)	\(64\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(86\)	\(6\)	\(80\)		\(83\)	\(6\)	\(77\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(88\)	\(7\)	\(81\)		\(85\)	\(7\)	\(78\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(76\)	\(7\)	\(69\)		\(73\)	\(7\)	\(66\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(89\)	\(7\)	\(82\)		\(86\)	\(7\)	\(79\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(77\)	\(7\)	\(70\)		\(74\)	\(7\)	\(67\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(75\)	\(6\)	\(69\)		\(72\)	\(6\)	\(66\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(87\)	\(8\)	\(79\)		\(84\)	\(8\)	\(76\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(81\)	\(8\)	\(73\)		\(78\)	\(8\)	\(70\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(85\)	\(6\)	\(79\)		\(82\)	\(6\)	\(76\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(83\)	\(4\)	\(79\)		\(80\)	\(4\)	\(76\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(79\)	\(8\)	\(71\)		\(76\)	\(8\)	\(68\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(82\)	\(5\)	\(77\)		\(79\)	\(5\)	\(74\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(78\)	\(9\)	\(69\)		\(75\)	\(9\)	\(66\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(80\)	\(9\)	\(71\)		\(77\)	\(9\)	\(68\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(84\)	\(3\)	\(81\)		\(81\)	\(3\)	\(78\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(636\)	\(46\)	\(590\)		\(613\)	\(46\)	\(567\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(668\)	\(62\)	\(606\)		\(644\)	\(62\)	\(582\)		\(24\)	\(0\)	\(24\)

Trace form

108 * q - 8 * q^5 - 4 * q^7 + 108 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^17 - 8 * q^23 + 116 * q^25 + 8 * q^29 + 8 * q^37 - 16 * q^39 + 8 * q^41 - 16 * q^43 - 8 * q^45 + 48 * q^47 + 108 * q^49 + 8 * q^53 - 32 * q^55 + 48 * q^59 - 8 * q^61 - 4 * q^63 + 48 * q^65 - 8 * q^67 - 8 * q^71 + 40 * q^73 - 32 * q^75 + 16 * q^77 + 40 * q^79 + 108 * q^81 - 16 * q^85 + 40 * q^89 + 8 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6384))\) 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	7	19
6384.2.a.a	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.l	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.b	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6384.2.a.c	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6384.2.a.d	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				1596.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
6384.2.a.e	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6384.2.a.f	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.m	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.g	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.h	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				1596.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.i	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6384.2.a.j	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.o	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots\)
6384.2.a.k	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.n	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6384.2.a.l	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				1596.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
6384.2.a.m	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.i	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.n	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.o	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.p	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
6384.2.a.p	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-4q^{15}+\cdots\)
6384.2.a.q	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				399.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6384.2.a.r	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{13}-4q^{15}+\cdots\)
6384.2.a.s	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.t	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6384.2.a.u	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.v	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.w	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.g	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.x	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				399.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+2q^{11}-4q^{17}+\cdots\)
6384.2.a.y	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.z	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				798.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.ba	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				1596.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6384.2.a.bb	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}+q^{21}+\cdots\)
6384.2.a.bc	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				399.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6384.2.a.bd	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				1596.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
6384.2.a.be	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.j	$1$	$1$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
6384.2.a.bf	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.i	$1$	$1$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6384.2.a.bg	$6384$	$2$	6384.a	1.a	$1$	$1$	$1$	$50.976$	\(\Q\)	None	✓				3192.2.a.h	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6384.2.a.bh	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{2}) \)	None	✓				3192.2.a.r	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{11}+\cdots\)
6384.2.a.bi	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.s	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
6384.2.a.bj	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{3}) \)	None	✓				1596.2.a.i	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bk	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.t	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{13}-\beta q^{15}+\cdots\)
6384.2.a.bl	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{5}) \)	None	✓				798.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bm	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{5}) \)	None	✓				1596.2.a.g	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bn	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{5}) \)	None	✓				798.2.a.j	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bo	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{7}) \)	None	✓				1596.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bp	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{2}) \)	None	✓				1596.2.a.h	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
6384.2.a.bq	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{2}) \)	None	✓				798.2.a.l	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots\)
6384.2.a.br	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{3}) \)	None	✓				798.2.a.k	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6384.2.a.bs	$6384$	$2$	6384.a	1.a	$1$	$2$	$2$	$50.976$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.q	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bt	$6384$	$2$	6384.a	1.a	$1$	$3$	$3$	$50.976$	3.3.1016.1	None	✓		✓		1596.2.a.j	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bu	$6384$	$2$	6384.a	1.a	$1$	$3$	$3$	$50.976$	3.3.404.1	None	✓		✓		399.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bv	$6384$	$2$	6384.a	1.a	$1$	$3$	$3$	$50.976$	3.3.316.1	None	✓		✓		3192.2.a.v	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bw	$6384$	$2$	6384.a	1.a	$1$	$3$	$3$	$50.976$	3.3.568.1	None	✓				3192.2.a.u	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bx	$6384$	$2$	6384.a	1.a	$1$	$3$	$3$	$50.976$	3.3.148.1	None	✓		✓		399.2.a.d	$1$	$0$	\(0\)	\(3\)	\(4\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.by	$6384$	$2$	6384.a	1.a	$1$	$4$	$4$	$50.976$	4.4.2225.1	None	✓		✓		3192.2.a.z	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6384.2.a.bz	$6384$	$2$	6384.a	1.a	$1$	$4$	$4$	$50.976$	4.4.7232.1	None	✓		✓		3192.2.a.y	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
6384.2.a.ca	$6384$	$2$	6384.a	1.a	$1$	$4$	$4$	$50.976$	4.4.13068.1	None	✓		✓		3192.2.a.w	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.cb	$6384$	$2$	6384.a	1.a	$1$	$4$	$4$	$50.976$	4.4.9248.1	None	✓		✓		3192.2.a.x	$1$	$0$	\(0\)	\(4\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.cc	$6384$	$2$	6384.a	1.a	$1$	$5$	$5$	$50.976$	5.5.1240016.1	None	✓		✓		399.2.a.f	$1$	$0$	\(0\)	\(-5\)	\(-2\)	\(-5\)		$-$	$+$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
6384.2.a.cd	$6384$	$2$	6384.a	1.a	$1$	$5$	$5$	$50.976$	5.5.401584.1	None	✓		✓		3192.2.a.bb	$1$	$1$	\(0\)	\(-5\)	\(2\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.ce	$6384$	$2$	6384.a	1.a	$1$	$5$	$5$	$50.976$	5.5.135076.1	None	✓		✓		3192.2.a.ba	$1$	$0$	\(0\)	\(5\)	\(2\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
6384.2.a.cf	$6384$	$2$	6384.a	1.a	$1$	$5$	$5$	$50.976$	5.5.368464.1	None	✓		✓		399.2.a.g	$1$	$0$	\(0\)	\(5\)	\(4\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6384))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6384)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)