Space of modular forms of level 5184, weight 2, and trivial character

• Label: 5184.2.a
• Level: $5184$
• Weight: $2$
• Character orbit: 5184.a
• Rep. character: $\chi_{5184}(1,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $58$
• Sturm bound: $1728$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(1728\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5184))\).

	Total	New	Old
Modular forms	936	100	836
Cusp forms	793	92	701
Eisenstein series	143	8	135

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
\(+\)	\(+\)	\(+\)		\(228\)	\(23\)	\(205\)		\(193\)	\(21\)	\(172\)		\(35\)	\(2\)	\(33\)
\(+\)	\(-\)	\(-\)		\(240\)	\(27\)	\(213\)		\(204\)	\(25\)	\(179\)		\(36\)	\(2\)	\(34\)
\(-\)	\(+\)	\(-\)		\(240\)	\(27\)	\(213\)		\(204\)	\(25\)	\(179\)		\(36\)	\(2\)	\(34\)
\(-\)	\(-\)	\(+\)		\(228\)	\(23\)	\(205\)		\(192\)	\(21\)	\(171\)		\(36\)	\(2\)	\(34\)
Plus space		\(+\)		\(456\)	\(46\)	\(410\)		\(385\)	\(42\)	\(343\)		\(71\)	\(4\)	\(67\)
Minus space		\(-\)		\(480\)	\(54\)	\(426\)		\(408\)	\(50\)	\(358\)		\(72\)	\(4\)	\(68\)

Trace form

\( 92 q - 4 q^{13} + 80 q^{25} + 8 q^{37} + 72 q^{49} - 4 q^{61} - 8 q^{73} - 24 q^{85} + 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5184))\) 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
5184.2.a.a	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				288.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}+5q^{11}+2q^{13}-3q^{17}+\cdots\)
5184.2.a.b	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				288.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}-5q^{11}+2q^{13}-3q^{17}+\cdots\)
5184.2.a.c	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				162.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}+q^{13}+3q^{17}+4q^{19}+\cdots\)
5184.2.a.d	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				324.2.a.b	$1$	$2$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-6q^{11}-5q^{13}-3q^{17}+\cdots\)
5184.2.a.e	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				36.2.e.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}-3q^{11}+q^{13}+6q^{17}+\cdots\)
5184.2.a.f	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				36.2.e.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+3q^{11}+q^{13}+6q^{17}+\cdots\)
5184.2.a.g	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				324.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}+6q^{11}-5q^{13}-3q^{17}+\cdots\)
5184.2.a.h	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				162.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}+q^{13}+3q^{17}-4q^{19}+\cdots\)
5184.2.a.i	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				72.2.i.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+5q^{11}+5q^{13}+2q^{17}+\cdots\)
5184.2.a.j	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
5184.2.a.k	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				648.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{11}+5q^{13}+5q^{17}-8q^{19}+\cdots\)
5184.2.a.l	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				648.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}+5q^{13}+5q^{17}+8q^{19}+\cdots\)
5184.2.a.m	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
5184.2.a.n	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				72.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-5q^{11}+5q^{13}+2q^{17}+\cdots\)
5184.2.a.o	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				18.2.c.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{11}-2q^{13}-3q^{17}-q^{19}+\cdots\)
5184.2.a.p	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				18.2.c.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+3q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
5184.2.a.q	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				18.2.c.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\)
5184.2.a.r	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				18.2.c.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+3q^{11}-2q^{13}-3q^{17}+q^{19}+\cdots\)
5184.2.a.s	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				72.2.i.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-5q^{11}+5q^{13}-2q^{17}+\cdots\)
5184.2.a.t	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{11}-q^{13}-3q^{17}+\cdots\)
5184.2.a.u	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				648.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}+5q^{13}-5q^{17}+8q^{19}+\cdots\)
5184.2.a.v	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				648.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}+5q^{13}-5q^{17}-8q^{19}+\cdots\)
5184.2.a.w	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
5184.2.a.x	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				72.2.i.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+5q^{11}+5q^{13}-2q^{17}+\cdots\)
5184.2.a.y	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				162.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-4q^{7}+q^{13}-3q^{17}+4q^{19}+\cdots\)
5184.2.a.z	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				324.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}+6q^{11}-5q^{13}+3q^{17}+\cdots\)
5184.2.a.ba	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				36.2.e.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}+3q^{11}+q^{13}-6q^{17}+\cdots\)
5184.2.a.bb	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				36.2.e.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-3q^{11}+q^{13}-6q^{17}+\cdots\)
5184.2.a.bc	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				324.2.a.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}-6q^{11}-5q^{13}+3q^{17}+\cdots\)
5184.2.a.bd	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				162.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}+q^{13}-3q^{17}-4q^{19}+\cdots\)
5184.2.a.be	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				288.2.i.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}-5q^{11}+2q^{13}+3q^{17}+\cdots\)
5184.2.a.bf	$5184$	$2$	5184.a	1.a	$1$	$1$	$1$	$41.394$	\(\Q\)	None	✓				288.2.i.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}+5q^{11}+2q^{13}+3q^{17}+\cdots\)
5184.2.a.bg	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				648.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bh	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓				2592.2.a.i	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(-2+\beta )q^{5}+(-3+2\beta )q^{13}+(4+\cdots)q^{17}+\cdots\)
5184.2.a.bi	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				648.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bj	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bk	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				2592.2.a.m	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+\beta q^{11}-3q^{13}+5q^{17}+\cdots\)
5184.2.a.bl	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				288.2.i.d	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+\beta q^{11}+3q^{13}-4q^{17}+\cdots\)
5184.2.a.bm	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓				2592.2.a.k	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(-1+\beta )q^{5}+(3+\beta )q^{13}+(-1+2\beta )q^{17}+\cdots\)
5184.2.a.bn	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1-\beta )q^{7}+(-1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bo	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{33}) \)	None	✓				72.2.i.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(-2+\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
5184.2.a.bp	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{33}) \)	None	✓				72.2.i.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(2-\beta )q^{7}+q^{11}+(-2-\beta )q^{13}+\cdots\)
5184.2.a.bq	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				81.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2q^{7}-2\beta q^{11}+q^{13}+3\beta q^{17}+\cdots\)
5184.2.a.br	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				81.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2q^{7}+2\beta q^{11}+q^{13}+3\beta q^{17}+\cdots\)
5184.2.a.bs	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{33}) \)	None	✓				72.2.i.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
5184.2.a.bt	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{33}) \)	None	✓				72.2.i.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
5184.2.a.bu	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5184.2.a.bv	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				2592.2.a.m	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}-\beta q^{11}-3q^{13}-5q^{17}+\cdots\)
5184.2.a.bw	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓				2592.2.a.k	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(1+\beta )q^{5}+(3-\beta )q^{13}+(1+2\beta )q^{17}+\cdots\)
5184.2.a.bx	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				288.2.i.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+\beta q^{11}+3q^{13}+4q^{17}+\cdots\)
5184.2.a.by	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bz	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				648.2.a.e	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.ca	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓				2592.2.a.i	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(2+\beta )q^{5}+(-3-2\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
5184.2.a.cb	$5184$	$2$	5184.a	1.a	$1$	$2$	$2$	$41.394$	\(\Q(\sqrt{3}) \)	None	✓				648.2.a.e	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.cc	$5184$	$2$	5184.a	1.a	$1$	$4$	$4$	$41.394$	4.4.13068.1	None	✓		✓		288.2.i.f	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+\cdots\)
5184.2.a.cd	$5184$	$2$	5184.a	1.a	$1$	$4$	$4$	$41.394$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				2592.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3})q^{11}+\cdots\)
5184.2.a.ce	$5184$	$2$	5184.a	1.a	$1$	$4$	$4$	$41.394$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				2592.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)
5184.2.a.cf	$5184$	$2$	5184.a	1.a	$1$	$4$	$4$	$41.394$	4.4.13068.1	None	✓		✓		288.2.i.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5184)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\)\(^{\oplus 2}\)