Space of modular forms of level 9555, weight 2, and trivial character

• Label: 9555.2.a
• Level: $9555$
• Weight: $2$
• Character orbit: 9555.a
• Rep. character: $\chi_{9555}(1,\cdot)$
• Character field: $\Q$
• Dimension: $328$
• Newform subspaces: $77$
• Sturm bound: $3136$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9555.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 77 \)
Sturm bound:			\(3136\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(11\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9555))\).

	Total	New	Old
Modular forms	1600	328	1272
Cusp forms	1537	328	1209
Eisenstein series	63	0	63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(19\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(25\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(24\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(15\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(19\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(17\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(24\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(19\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(17\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(19\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(25\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(15\)
Plus space				\(+\)	\(144\)
Minus space				\(-\)	\(184\)

Trace form

\( 328 q - 8 q^{2} + 324 q^{4} + 4 q^{6} - 24 q^{8} + 328 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9555))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	7	13
9555.2.a.a	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
9555.2.a.b	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
9555.2.a.c	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
9555.2.a.d	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
9555.2.a.e	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
9555.2.a.f	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}+q^{9}+2q^{12}-q^{13}+\cdots\)
9555.2.a.g	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}+q^{9}+q^{11}+2q^{12}+\cdots\)
9555.2.a.h	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+q^{9}+2q^{12}+q^{13}+\cdots\)
9555.2.a.i	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+q^{9}+5q^{11}+2q^{12}+\cdots\)
9555.2.a.j	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{9}-2q^{12}-q^{13}+\cdots\)
9555.2.a.k	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{9}+5q^{11}-2q^{12}+\cdots\)
9555.2.a.l	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+q^{9}-2q^{12}+q^{13}+\cdots\)
9555.2.a.m	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots\)
9555.2.a.n	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
9555.2.a.o	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
9555.2.a.p	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
9555.2.a.q	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
9555.2.a.r	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
9555.2.a.s	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
9555.2.a.t	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
9555.2.a.u	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
9555.2.a.v	$9555$	$2$	9555.a	1.a	$1$	$1$	$1$	$76.297$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
9555.2.a.w	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-3\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\)
9555.2.a.x	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$2$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
9555.2.a.y	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
9555.2.a.z	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
9555.2.a.ba	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
9555.2.a.bb	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
9555.2.a.bc	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
9555.2.a.bd	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
9555.2.a.be	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
9555.2.a.bf	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
9555.2.a.bg	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
9555.2.a.bh	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
9555.2.a.bi	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
9555.2.a.bj	$9555$	$2$	9555.a	1.a	$1$	$2$	$2$	$76.297$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
9555.2.a.bk	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.bl	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.837.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.bm	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.621.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9555.2.a.bn	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.bo	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.bp	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.621.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9555.2.a.bq	$9555$	$2$	9555.a	1.a	$1$	$3$	$3$	$76.297$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(3+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.br	$9555$	$2$	9555.a	1.a	$1$	$4$	$4$	$76.297$	4.4.2225.1	None	✓	$1$	$1$	\(-3\)	\(-4\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9555.2.a.bs	$9555$	$2$	9555.a	1.a	$1$	$4$	$4$	$76.297$	4.4.8768.1	None	✓	$1$	$0$	\(-2\)	\(-4\)	\(-4\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9555.2.a.bt	$9555$	$2$	9555.a	1.a	$1$	$4$	$4$	$76.297$	4.4.8768.1	None	✓	$1$	$1$	\(-2\)	\(4\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9555.2.a.bu	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.70601.1	None	✓	$1$	$1$	\(-1\)	\(-5\)	\(-5\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
9555.2.a.bv	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.70601.1	None	✓	$1$	$1$	\(-1\)	\(-5\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
9555.2.a.bw	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.70601.1	None	✓	$1$	$1$	\(-1\)	\(5\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
9555.2.a.bx	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.70601.1	None	✓	$1$	$1$	\(-1\)	\(5\)	\(5\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
9555.2.a.by	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.255877.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(-5\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{3}+(2+\beta _{1})q^{4}-q^{5}+\beta _{2}q^{6}+\cdots\)
9555.2.a.bz	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.2290624.1	None	✓	$1$	$1$	\(1\)	\(-5\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.ca	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.2290624.1	None	✓	$1$	$0$	\(1\)	\(5\)	\(5\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.cb	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.990009.1	None	✓	$1$	$0$	\(3\)	\(-5\)	\(5\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+q^{5}+\cdots\)
9555.2.a.cc	$9555$	$2$	9555.a	1.a	$1$	$5$	$5$	$76.297$	5.5.990009.1	None	✓	$1$	$0$	\(3\)	\(5\)	\(-5\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}-q^{5}+\cdots\)
9555.2.a.cd	$9555$	$2$	9555.a	1.a	$1$	$6$	$6$	$76.297$	6.6.224086784.1	None	✓	$1$	$0$	\(-2\)	\(-6\)	\(6\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.ce	$9555$	$2$	9555.a	1.a	$1$	$6$	$6$	$76.297$	6.6.224086784.1	None	✓	$1$	$1$	\(-2\)	\(6\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cf	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-7\)	\(7\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.cg	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-7\)	\(7\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.ch	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-7\)	\(7\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.ci	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(7\)	\(-7\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cj	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(7\)	\(-7\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.ck	$9555$	$2$	9555.a	1.a	$1$	$7$	$7$	$76.297$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(7\)	\(-7\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cl	$9555$	$2$	9555.a	1.a	$1$	$8$	$8$	$76.297$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8\)	\(8\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.cm	$9555$	$2$	9555.a	1.a	$1$	$8$	$8$	$76.297$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(8\)	\(-8\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cn	$9555$	$2$	9555.a	1.a	$1$	$8$	$8$	$76.297$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(-8\)	\(-8\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
9555.2.a.co	$9555$	$2$	9555.a	1.a	$1$	$8$	$8$	$76.297$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(8\)	\(8\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
9555.2.a.cp	$9555$	$2$	9555.a	1.a	$1$	$9$	$9$	$76.297$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-9\)	\(9\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9555.2.a.cq	$9555$	$2$	9555.a	1.a	$1$	$9$	$9$	$76.297$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(9\)	\(-9\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9555.2.a.cr	$9555$	$2$	9555.a	1.a	$1$	$10$	$10$	$76.297$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-10\)	\(10\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.cs	$9555$	$2$	9555.a	1.a	$1$	$10$	$10$	$76.297$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(10\)	\(-10\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.ct	$9555$	$2$	9555.a	1.a	$1$	$10$	$10$	$76.297$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-10\)	\(-10\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cu	$9555$	$2$	9555.a	1.a	$1$	$10$	$10$	$76.297$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(10\)	\(10\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9555.2.a.cv	$9555$	$2$	9555.a	1.a	$1$	$14$	$14$	$76.297$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(-6\)	\(-14\)	\(-14\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9555.2.a.cw	$9555$	$2$	9555.a	1.a	$1$	$14$	$14$	$76.297$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(14\)	\(14\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9555.2.a.cx	$9555$	$2$	9555.a	1.a	$1$	$14$	$14$	$76.297$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(-14\)	\(-14\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9555.2.a.cy	$9555$	$2$	9555.a	1.a	$1$	$14$	$14$	$76.297$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(14\)	\(14\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9555))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9555)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3185))\)\(^{\oplus 2}\)