Space of modular forms of level 6864, weight 2, and trivial character

• Label: 6864.2.a
• Level: $6864$
• Weight: $2$
• Character orbit: 6864.a
• Rep. character: $\chi_{6864}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $58$
• Sturm bound: $2688$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6864.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6864))\).

	Total	New	Old
Modular forms	1368	120	1248
Cusp forms	1321	120	1201
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.

\(2\)	\(3\)	\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(73\)	\(7\)	\(66\)		\(71\)	\(7\)	\(64\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(98\)	\(9\)	\(89\)		\(95\)	\(9\)	\(86\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(92\)	\(8\)	\(84\)		\(89\)	\(8\)	\(81\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(79\)	\(6\)	\(73\)		\(76\)	\(6\)	\(70\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(83\)	\(8\)	\(75\)		\(80\)	\(8\)	\(72\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(88\)	\(6\)	\(82\)		\(85\)	\(6\)	\(79\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(94\)	\(7\)	\(87\)		\(91\)	\(7\)	\(84\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(77\)	\(9\)	\(68\)		\(74\)	\(9\)	\(65\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(84\)	\(8\)	\(76\)		\(81\)	\(8\)	\(73\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(87\)	\(6\)	\(81\)		\(84\)	\(6\)	\(78\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(85\)	\(7\)	\(78\)		\(82\)	\(7\)	\(75\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(86\)	\(9\)	\(77\)		\(83\)	\(9\)	\(74\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(82\)	\(7\)	\(75\)		\(79\)	\(7\)	\(72\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(89\)	\(9\)	\(80\)		\(86\)	\(9\)	\(77\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(91\)	\(8\)	\(83\)		\(88\)	\(8\)	\(80\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(80\)	\(6\)	\(74\)		\(77\)	\(6\)	\(71\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(668\)	\(52\)	\(616\)		\(645\)	\(52\)	\(593\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(700\)	\(68\)	\(632\)		\(676\)	\(68\)	\(608\)		\(24\)	\(0\)	\(24\)

Trace form

120 * q + 120 * q^9 - 8 * q^15 - 16 * q^19 + 120 * q^25 - 40 * q^31 - 48 * q^35 - 48 * q^47 + 120 * q^49 - 16 * q^51 + 32 * q^61 - 24 * q^67 + 32 * q^69 + 48 * q^71 - 16 * q^79 + 120 * q^81 + 48 * q^83 + 32 * q^85 + 24 * q^91

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6864))\) 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	11	13
6864.2.a.a	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.j	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(-5\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.b	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.d	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-3q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.c	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.d	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots\)
6864.2.a.e	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				429.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots\)
6864.2.a.f	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				1716.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.g	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.k	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.h	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				1716.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+q^{11}+q^{13}+6q^{17}+\cdots\)
6864.2.a.i	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-q^{11}-q^{13}-4q^{17}+\cdots\)
6864.2.a.j	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}+q^{11}+q^{13}+4q^{19}+\cdots\)
6864.2.a.k	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.l	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.l	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.m	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.n	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.o	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.p	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.m	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.q	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.r	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.s	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.t	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.u	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.g	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.v	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				3432.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+q^{11}-q^{13}+8q^{17}+\cdots\)
6864.2.a.w	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				429.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-q^{11}+q^{13}-4q^{17}+\cdots\)
6864.2.a.x	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				1716.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+q^{11}+q^{13}-2q^{17}+\cdots\)
6864.2.a.y	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.h	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.z	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots\)
6864.2.a.ba	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	\(\Q\)	None	✓				858.2.a.i	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}-q^{11}+q^{13}+4q^{15}+\cdots\)
6864.2.a.bb	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{2}) \)	None	✓				1716.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
6864.2.a.bc	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{2}) \)	None	✓				429.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots\)
6864.2.a.bd	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{41}) \)	None	✓				858.2.a.p	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.be	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{2}) \)	None	✓				3432.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.bf	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{41}) \)	None	✓				858.2.a.q	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.bg	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{6}) \)	None	✓				3432.2.a.j	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.bh	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{17}) \)	None	✓				858.2.a.n	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
6864.2.a.bi	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{3}) \)	None	✓				1716.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.bj	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{5}) \)	None	✓				3432.2.a.k	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.bk	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{3}) \)	None	✓				429.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+2q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.bl	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{33}) \)	None	✓				858.2.a.o	$1$	$0$	\(0\)	\(2\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.bm	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	\(\Q(\sqrt{3}) \)	None	✓				3432.2.a.l	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.bn	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.404.1	None	✓				3432.2.a.n	$1$	$0$	\(0\)	\(-3\)	\(-4\)	\(6\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6864.2.a.bo	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.892.1	None	✓		✓		3432.2.a.o	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(-5\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6864.2.a.bp	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓		✓		429.2.a.f	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.bq	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓				3432.2.a.p	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.br	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.564.1	None	✓		✓		1716.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
6864.2.a.bs	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓		✓		429.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(4\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6864.2.a.bt	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.404.1	None	✓		✓		1716.2.a.h	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
6864.2.a.bu	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.564.1	None	✓		✓		429.2.a.e	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
6864.2.a.bv	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.1620.1	None	✓		✓		1716.2.a.f	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.bw	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.70164.1	None	✓		✓		3432.2.a.u	$1$	$1$	\(0\)	\(-4\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)
6864.2.a.bx	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.83476.1	None	✓		✓		3432.2.a.v	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
6864.2.a.by	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.22676.1	None	✓		✓		3432.2.a.q	$1$	$1$	\(0\)	\(4\)	\(-3\)	\(-3\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
6864.2.a.bz	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.8468.1	None	✓		✓		429.2.a.h	$1$	$1$	\(0\)	\(4\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots\)
6864.2.a.ca	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.70164.1	None	✓				3432.2.a.r	$1$	$0$	\(0\)	\(4\)	\(1\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
6864.2.a.cb	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.90996.1	None	✓		✓		1716.2.a.i	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.cc	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.23252.1	None	✓				3432.2.a.t	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.cd	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.29268.1	None	✓				3432.2.a.s	$1$	$0$	\(0\)	\(4\)	\(4\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.ce	$6864$	$2$	6864.a	1.a	$1$	$5$	$5$	$54.809$	5.5.46437524.1	None	✓		✓		3432.2.a.x	$1$	$0$	\(0\)	\(-5\)	\(1\)	\(3\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.cf	$6864$	$2$	6864.a	1.a	$1$	$5$	$5$	$54.809$	5.5.2172244.1	None	✓		✓		3432.2.a.w	$1$	$0$	\(0\)	\(5\)	\(1\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6864)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3432))\)\(^{\oplus 2}\)