Space of modular forms of level 5824, weight 2, and trivial character

• Label: 5824.2.a
• Level: $5824$
• Weight: $2$
• Character orbit: 5824.a
• Rep. character: $\chi_{5824}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $66$
• Sturm bound: $1792$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5824 = 2^{6} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5824.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 66 \)
Sturm bound:			\(1792\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5824))\).

	Total	New	Old
Modular forms	920	144	776
Cusp forms	873	144	729
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.

\(2\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(+\)	\(-\)	$-$	\(20\)
\(+\)	\(-\)	\(+\)	$-$	\(19\)
\(+\)	\(-\)	\(-\)	$+$	\(16\)
\(-\)	\(+\)	\(+\)	$-$	\(19\)
\(-\)	\(+\)	\(-\)	$+$	\(16\)
\(-\)	\(-\)	\(+\)	$+$	\(17\)
\(-\)	\(-\)	\(-\)	$-$	\(20\)
Plus space			\(+\)	\(66\)
Minus space			\(-\)	\(78\)

Trace form

\( 144 q + 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5824))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	13
5824.2.a.a	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{7}+6q^{9}+5q^{11}+q^{13}+\cdots\)
5824.2.a.b	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+4q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
5824.2.a.c	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{5}+q^{7}+q^{9}+q^{13}+6q^{15}+\cdots\)
5824.2.a.d	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
5824.2.a.e	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
5824.2.a.f	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}-6q^{15}+\cdots\)
5824.2.a.g	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
5824.2.a.h	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}-2q^{9}-5q^{11}+\cdots\)
5824.2.a.i	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}+q^{11}-q^{13}+4q^{17}+\cdots\)
5824.2.a.j	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
5824.2.a.k	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
5824.2.a.l	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
5824.2.a.m	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
5824.2.a.n	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
5824.2.a.o	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
5824.2.a.p	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}+4q^{11}-q^{13}+\cdots\)
5824.2.a.q	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
5824.2.a.r	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
5824.2.a.s	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots\)
5824.2.a.t	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-3q^{9}-6q^{11}+q^{13}+\cdots\)
5824.2.a.u	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
5824.2.a.v	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots\)
5824.2.a.w	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
5824.2.a.x	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
5824.2.a.y	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots\)
5824.2.a.z	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}-q^{11}-q^{13}+4q^{17}+\cdots\)
5824.2.a.ba	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-q^{7}+q^{9}+q^{13}-6q^{15}+\cdots\)
5824.2.a.bb	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
5824.2.a.bc	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
5824.2.a.bd	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{13}+6q^{15}+\cdots\)
5824.2.a.be	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{7}+6q^{9}-5q^{11}+q^{13}+\cdots\)
5824.2.a.bf	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}+q^{7}+6q^{9}+q^{11}+\cdots\)
5824.2.a.bg	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
5824.2.a.bh	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
5824.2.a.bi	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
5824.2.a.bj	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
5824.2.a.bk	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-3+\beta )q^{5}-q^{7}-q^{9}+3\beta q^{11}+\cdots\)
5824.2.a.bl	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-3-\beta )q^{5}+q^{7}-q^{9}+3\beta q^{11}+\cdots\)
5824.2.a.bm	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{5}-q^{7}+3q^{9}+(-4+\cdots)q^{11}+\cdots\)
5824.2.a.bn	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+3q^{9}+(4+\cdots)q^{11}+\cdots\)
5824.2.a.bo	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
5824.2.a.bp	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
5824.2.a.bq	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
5824.2.a.br	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+4\beta )q^{9}+\cdots\)
5824.2.a.bs	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+\cdots\)
5824.2.a.bt	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.564.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5824.2.a.bu	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
5824.2.a.bv	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
5824.2.a.bw	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(5\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(2-\beta _{1})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.bx	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(5\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.by	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+\cdots\)
5824.2.a.bz	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.564.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5824.2.a.ca	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.11348.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.cb	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.64268.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cc	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.183064.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5824.2.a.cd	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.33844.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5824.2.a.ce	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.64268.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cf	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.183064.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5824.2.a.cg	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.33844.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5824.2.a.ch	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.11348.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.ci	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.1025428.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(1-\beta _{4})q^{5}-q^{7}+\cdots\)
5824.2.a.cj	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.6329476.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-5\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.ck	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.6329476.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.cl	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.1025428.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(1-\beta _{4})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
5824.2.a.cm	$5824$	$2$	5824.a	1.a	$1$	$6$	$6$	$46.505$	6.6.153499364.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(6\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cn	$5824$	$2$	5824.a	1.a	$1$	$6$	$6$	$46.505$	6.6.153499364.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-3\)	\(-6\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5824))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5824)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2912))\)\(^{\oplus 2}\)