Space of modular forms of level 8496, weight 2, and trivial character

• Label: 8496.2.a
• Level: $8496$
• Weight: $2$
• Character orbit: 8496.a
• Rep. character: $\chi_{8496}(1,\cdot)$
• Character field: $\Q$
• Dimension: $145$
• Newform subspaces: $56$
• Sturm bound: $2880$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8496 = 2^{4} \cdot 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8496.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(2880\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8496))\).

	Total	New	Old
Modular forms	1464	145	1319
Cusp forms	1417	145	1272
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.

\(2\)	\(3\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(15\)
\(+\)	\(+\)	\(-\)	$-$	\(15\)
\(+\)	\(-\)	\(+\)	$-$	\(26\)
\(+\)	\(-\)	\(-\)	$+$	\(17\)
\(-\)	\(+\)	\(+\)	$-$	\(14\)
\(-\)	\(+\)	\(-\)	$+$	\(14\)
\(-\)	\(-\)	\(+\)	$+$	\(22\)
\(-\)	\(-\)	\(-\)	$-$	\(22\)
Plus space			\(+\)	\(68\)
Minus space			\(-\)	\(77\)

Trace form

\( 145 q - 2 q^{5} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8496))\) 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	3	59
8496.2.a.a	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-4q^{11}+2q^{13}-4q^{17}+\cdots\)
8496.2.a.b	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{11}+2q^{17}-4q^{19}+4q^{23}+\cdots\)
8496.2.a.c	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+6q^{11}-4q^{13}+6q^{17}+\cdots\)
8496.2.a.d	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)
8496.2.a.e	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}+4q^{19}-q^{25}-6q^{29}+\cdots\)
8496.2.a.f	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}-6q^{13}-2q^{17}-4q^{19}+\cdots\)
8496.2.a.g	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+3q^{7}+q^{11}+3q^{13}+q^{17}+\cdots\)
8496.2.a.h	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+2q^{11}-6q^{13}+2q^{17}+\cdots\)
8496.2.a.i	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots\)
8496.2.a.j	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-5q^{11}+q^{13}-q^{17}-6q^{23}+\cdots\)
8496.2.a.k	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+3q^{11}+5q^{13}+3q^{17}-8q^{19}+\cdots\)
8496.2.a.l	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}-2q^{13}+4q^{17}-5q^{25}+\cdots\)
8496.2.a.m	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}-2q^{13}-4q^{17}-5q^{25}+\cdots\)
8496.2.a.n	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-4q^{11}+6q^{13}+6q^{17}+\cdots\)
8496.2.a.o	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{13}+6q^{17}-3q^{19}+\cdots\)
8496.2.a.p	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
8496.2.a.q	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-2q^{11}-2q^{17}+5q^{19}+\cdots\)
8496.2.a.r	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
8496.2.a.s	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}+4q^{19}-q^{25}+6q^{29}+\cdots\)
8496.2.a.t	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+3q^{7}-q^{11}-3q^{13}-7q^{17}+\cdots\)
8496.2.a.u	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{7}+6q^{11}-6q^{13}+2q^{17}+\cdots\)
8496.2.a.v	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
8496.2.a.w	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{7}+4q^{11}+2q^{13}+4q^{17}+\cdots\)
8496.2.a.x	$8496$	$2$	8496.a	1.a	$1$	$1$	$1$	$67.841$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}-3q^{11}-q^{13}+7q^{17}+\cdots\)
8496.2.a.y	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{61}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+\beta q^{7}+q^{11}+q^{13}+(-3+\cdots)q^{17}+\cdots\)
8496.2.a.z	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{11}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-4q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
8496.2.a.ba	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(1+2\beta )q^{11}-q^{13}+\cdots\)
8496.2.a.bb	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{5}+(3+\beta )q^{7}+(1-2\beta )q^{11}+\cdots\)
8496.2.a.bc	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1-\beta )q^{7}+(3-2\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8496.2.a.bd	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(2-\beta )q^{7}+(-1-2\beta )q^{11}+\cdots\)
8496.2.a.be	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(2-\beta )q^{7}-q^{11}-3q^{13}+(-1+\cdots)q^{17}+\cdots\)
8496.2.a.bf	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+2\beta )q^{5}+(2-3\beta )q^{7}-5q^{11}+\cdots\)
8496.2.a.bg	$8496$	$2$	8496.a	1.a	$1$	$2$	$2$	$67.841$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+(3+\beta )q^{7}+(1-4\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8496.2.a.bh	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8496.2.a.bi	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8496.2.a.bj	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.733.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
8496.2.a.bk	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.621.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(\beta _{1}+\beta _{2})q^{7}-3q^{11}+(1+\cdots)q^{13}+\cdots\)
8496.2.a.bl	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{5}+(-3-\beta _{1})q^{7}+\cdots\)
8496.2.a.bm	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+(-3-\beta _{2})q^{7}+2\beta _{1}q^{11}+\cdots\)
8496.2.a.bn	$8496$	$2$	8496.a	1.a	$1$	$3$	$3$	$67.841$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+(1+2\beta _{1}+\cdots)q^{11}+\cdots\)
8496.2.a.bo	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.27004.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-1\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+(-1+\beta _{3})q^{11}+\cdots\)
8496.2.a.bp	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.22896.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{5}-\beta _{3}q^{7}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
8496.2.a.bq	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.106272.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+\beta _{2}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
8496.2.a.br	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.106272.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}+(2+\beta _{2})q^{11}+(2+\cdots)q^{13}+\cdots\)
8496.2.a.bs	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.22896.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{5}-\beta _{3}q^{7}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)
8496.2.a.bt	$8496$	$2$	8496.a	1.a	$1$	$4$	$4$	$67.841$	4.4.6809.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{3})q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
8496.2.a.bu	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.246832.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}-\beta _{3})q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
8496.2.a.bv	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.138136.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{4})q^{7}+\cdots\)
8496.2.a.bw	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.1815152.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
8496.2.a.bx	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.5755900.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+(\beta _{3}-\beta _{4})q^{11}+\cdots\)
8496.2.a.by	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.1815152.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
8496.2.a.bz	$8496$	$2$	8496.a	1.a	$1$	$5$	$5$	$67.841$	5.5.246832.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}+\beta _{3})q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
8496.2.a.ca	$8496$	$2$	8496.a	1.a	$1$	$6$	$6$	$67.841$	6.6.921465377.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-7\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(1+\beta _{4})q^{7}-\beta _{3}q^{11}+\cdots\)
8496.2.a.cb	$8496$	$2$	8496.a	1.a	$1$	$6$	$6$	$67.841$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-1+\beta _{3})q^{7}-\beta _{5}q^{11}+\cdots\)
8496.2.a.cc	$8496$	$2$	8496.a	1.a	$1$	$8$	$8$	$67.841$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(1-\beta _{1}+\beta _{4}+\cdots)q^{11}+\cdots\)
8496.2.a.cd	$8496$	$2$	8496.a	1.a	$1$	$8$	$8$	$67.841$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}-\beta _{6}q^{7}+(-1+\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(354))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(472))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(531))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(708))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(944))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1062))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4248))\)\(^{\oplus 2}\)