Space of modular forms of level 8784, weight 2, and trivial character

• Label: 8784.2.a
• Level: $8784$
• Weight: $2$
• Character orbit: 8784.a
• Rep. character: $\chi_{8784}(1,\cdot)$
• Character field: $\Q$
• Dimension: $150$
• Newform subspaces: $58$
• Sturm bound: $2976$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8784 = 2^{4} \cdot 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8784.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2976\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8784))\).

	Total	New	Old
Modular forms	1512	150	1362
Cusp forms	1465	150	1315
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.

\(2\)	\(3\)	\(61\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(+\)	\(-\)	$-$	\(18\)
\(+\)	\(-\)	\(+\)	$-$	\(24\)
\(+\)	\(-\)	\(-\)	$+$	\(21\)
\(-\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(-\)	$+$	\(12\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(24\)
Plus space			\(+\)	\(66\)
Minus space			\(-\)	\(84\)

Trace form

\( 150 q - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8784))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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	61
8784.2.a.a	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.d	$1$	$2$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-6q^{11}+4q^{13}-5q^{17}+\cdots\)
8784.2.a.b	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1098.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{11}-2q^{13}-q^{17}-2q^{19}+\cdots\)
8784.2.a.c	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		732.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
8784.2.a.d	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1098.2.a.d	$1$	$2$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-6q^{11}-6q^{13}+3q^{17}+\cdots\)
8784.2.a.e	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-3q^{11}-5q^{13}+6q^{17}+\cdots\)
8784.2.a.f	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots\)
8784.2.a.g	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+2q^{11}+4q^{13}+7q^{17}+\cdots\)
8784.2.a.h	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+6q^{11}-3q^{17}-q^{23}+\cdots\)
8784.2.a.i	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-5q^{11}-q^{13}-2q^{17}+\cdots\)
8784.2.a.j	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		122.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{7}-3q^{11}-3q^{13}+5q^{23}+\cdots\)
8784.2.a.k	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		732.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{7}+5q^{11}+q^{13}+6q^{17}+\cdots\)
8784.2.a.l	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		2196.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
8784.2.a.m	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		2196.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
8784.2.a.n	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		549.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
8784.2.a.o	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		549.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+4q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
8784.2.a.p	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1098.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+6q^{11}-6q^{13}-3q^{17}+\cdots\)
8784.2.a.q	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.e	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+2q^{11}+4q^{13}-q^{17}+\cdots\)
8784.2.a.r	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
8784.2.a.s	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-2q^{11}+2q^{13}-4q^{17}+\cdots\)
8784.2.a.t	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}+2q^{13}+4q^{17}+4q^{19}+\cdots\)
8784.2.a.u	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1464.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{13}-6q^{17}-4q^{19}+4q^{23}+\cdots\)
8784.2.a.v	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		732.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-6q^{13}-4q^{23}-q^{25}+\cdots\)
8784.2.a.w	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		61.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-5q^{11}+q^{13}-4q^{17}+\cdots\)
8784.2.a.x	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		1098.2.a.f	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{11}-2q^{13}+q^{17}-2q^{19}+\cdots\)
8784.2.a.y	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots\)
8784.2.a.z	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		366.2.a.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots\)
8784.2.a.ba	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	\(\Q\)	None	✓		244.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{7}-q^{11}+q^{13}+2q^{17}+\cdots\)
8784.2.a.bb	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{6}) \)	None	✓		1464.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+(1-\beta )q^{7}+(3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
8784.2.a.bc	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{3}) \)	None	✓		732.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
8784.2.a.bd	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{13}) \)	None	✓		122.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-3+\beta )q^{7}+(2-2\beta )q^{11}+(4-2\beta )q^{13}+\cdots\)
8784.2.a.be	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{3}) \)	None	✓		732.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}-2q^{7}+(3-\beta )q^{11}+(2+2\beta )q^{13}+\cdots\)
8784.2.a.bf	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{3}) \)	None	✓		549.2.a.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}-3\beta q^{11}+5q^{13}+2\beta q^{17}+\cdots\)
8784.2.a.bg	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{17}) \)	None	✓		366.2.a.h	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
8784.2.a.bh	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{2}) \)	None	✓		488.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(-1+3\beta )q^{11}+\cdots\)
8784.2.a.bi	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{2}) \)	None	✓		183.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}-3q^{13}+\cdots\)
8784.2.a.bj	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	\(\Q(\sqrt{6}) \)	None	✓		1464.2.a.g	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2\beta q^{7}+(-2-\beta )q^{11}+4q^{13}+\cdots\)
8784.2.a.bk	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		183.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots\)
8784.2.a.bl	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.892.1	None	✓		1098.2.a.o	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}+(1-\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8784.2.a.bm	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.229.1	None	✓		122.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8784.2.a.bn	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		61.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{11}+\cdots\)
8784.2.a.bo	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		488.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(2+\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
8784.2.a.bp	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.961.1	None	✓		1464.2.a.i	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\)
8784.2.a.bq	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.1304.1	None	✓		732.2.a.f	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(-1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots\)
8784.2.a.br	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.892.1	None	✓		1098.2.a.o	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+(1-\beta _{1})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
8784.2.a.bs	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.15317.1	None	✓		1464.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-1\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}+(1-\beta _{3})q^{11}+\cdots\)
8784.2.a.bt	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.20308.1	None	✓		244.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}-\beta _{3}q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots\)
8784.2.a.bu	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.7232.1	None	✓		1464.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
8784.2.a.bv	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.13676.1	None	✓		488.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{1})q^{7}+\cdots\)
8784.2.a.bw	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.9248.1	None	✓		1464.2.a.k	$1$	$0$	\(0\)	\(0\)	\(6\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
8784.2.a.bx	$8784$	$2$	8784.a	1.a	$1$	$5$	$5$	$70.141$	5.5.4383968.1	None	✓		1464.2.a.m	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
8784.2.a.by	$8784$	$2$	8784.a	1.a	$1$	$6$	$6$	$70.141$	6.6.643168996.1	None	✓		488.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{4})q^{5}+(-1+\beta _{3})q^{7}-\beta _{5}q^{11}+\cdots\)
8784.2.a.bz	$8784$	$2$	8784.a	1.a	$1$	$6$	$6$	$70.141$	6.6.53729968.1	None	✓		4392.2.a.r	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+\beta _{4}q^{7}+(\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
8784.2.a.ca	$8784$	$2$	8784.a	1.a	$1$	$6$	$6$	$70.141$	6.6.91407488.1	None	✓		183.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}-\beta _{5}q^{7}+(-2-\beta _{4}+\beta _{5})q^{11}+\cdots\)
8784.2.a.cb	$8784$	$2$	8784.a	1.a	$1$	$6$	$6$	$70.141$	6.6.337383424.1	None	✓		549.2.a.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{5}+(-1+\beta _{1})q^{7}-\beta _{3}q^{11}+\cdots\)
8784.2.a.cc	$8784$	$2$	8784.a	1.a	$1$	$6$	$6$	$70.141$	6.6.53729968.1	None	✓		4392.2.a.r	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+\beta _{4}q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
8784.2.a.cd	$8784$	$2$	8784.a	1.a	$1$	$8$	$8$	$70.141$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		2196.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{5}+(\beta _{2}+\beta _{7})q^{7}+(\beta _{1}-\beta _{5})q^{11}+\cdots\)
8784.2.a.ce	$8784$	$2$	8784.a	1.a	$1$	$9$	$9$	$70.141$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		4392.2.a.t	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{5}-\beta _{2}q^{7}+(1-\beta _{4})q^{11}+(-\beta _{5}+\cdots)q^{13}+\cdots\)
8784.2.a.cf	$8784$	$2$	8784.a	1.a	$1$	$9$	$9$	$70.141$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		4392.2.a.t	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{5}-\beta _{2}q^{7}+(-1+\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8784))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8784)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(244))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(366))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(488))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(549))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(732))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(976))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1098))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2928))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4392))\)\(^{\oplus 2}\)