Space of modular forms of level 4550, weight 2, and trivial character

• Label: 4550.2.a
• Level: $4550$
• Weight: $2$
• Character orbit: 4550.a
• Rep. character: $\chi_{4550}(1,\cdot)$
• Character field: $\Q$
• Dimension: $114$
• Newform subspaces: $56$
• Sturm bound: $1680$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4550 = 2 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4550.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(1680\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4550))\).

	Total	New	Old
Modular forms	864	114	750
Cusp forms	817	114	703
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.

\(2\)	\(5\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(5\)
Plus space				\(+\)	\(42\)
Minus space				\(-\)	\(72\)

Trace form

\( 114 q + 2 q^{2} - 4 q^{3} + 114 q^{4} + 4 q^{6} + 2 q^{8} + 110 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4550))\) 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	5	7	13
4550.2.a.a	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}+3q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.b	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.c	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.d	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.e	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+q^{13}+\cdots\)
4550.2.a.f	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-6q^{11}+\cdots\)
4550.2.a.g	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
4550.2.a.h	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.i	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.j	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.k	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.l	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.m	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.n	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.o	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.p	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.q	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.r	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.s	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.t	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4550.2.a.u	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4550.2.a.v	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-2q^{11}+\cdots\)
4550.2.a.w	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}+4q^{11}+\cdots\)
4550.2.a.x	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{13}+\cdots\)
4550.2.a.y	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.z	$4550$	$2$	4550.a	1.a	$1$	$1$	$1$	$36.332$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.ba	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.bb	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.bc	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
4550.2.a.bd	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4550.2.a.be	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
4550.2.a.bf	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
4550.2.a.bg	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
4550.2.a.bh	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
4550.2.a.bi	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4550.2.a.bj	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
4550.2.a.bk	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
4550.2.a.bl	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
4550.2.a.bm	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.bn	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.bo	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(2\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
4550.2.a.bp	$4550$	$2$	4550.a	1.a	$1$	$2$	$2$	$36.332$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(2\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
4550.2.a.bq	$4550$	$2$	4550.a	1.a	$1$	$3$	$3$	$36.332$	3.3.785.1	None	✓	$1$	$0$	\(-3\)	\(-2\)	\(0\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
4550.2.a.br	$4550$	$2$	4550.a	1.a	$1$	$3$	$3$	$36.332$	3.3.229.1	None	✓	$1$	$0$	\(-3\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-q^{7}+\cdots\)
4550.2.a.bs	$4550$	$2$	4550.a	1.a	$1$	$3$	$3$	$36.332$	3.3.568.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(0\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+q^{7}+\cdots\)
4550.2.a.bt	$4550$	$2$	4550.a	1.a	$1$	$3$	$3$	$36.332$	3.3.785.1	None	✓	$1$	$0$	\(3\)	\(2\)	\(0\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
4550.2.a.bu	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.222433.1	None	✓	$1$	$0$	\(-4\)	\(-3\)	\(0\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
4550.2.a.bv	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.10304.1	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
4550.2.a.bw	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.78441.1	None	✓	$1$	$0$	\(-4\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)
4550.2.a.bx	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.78441.1	None	✓	$1$	$0$	\(4\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
4550.2.a.by	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.10304.1	None	✓	$1$	$0$	\(4\)	\(2\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
4550.2.a.bz	$4550$	$2$	4550.a	1.a	$1$	$4$	$4$	$36.332$	4.4.222433.1	None	✓	$1$	$0$	\(4\)	\(3\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
4550.2.a.ca	$4550$	$2$	4550.a	1.a	$1$	$5$	$5$	$36.332$	5.5.117688.1	None	✓	$1$	$1$	\(-5\)	\(-4\)	\(0\)	\(5\)		$+$	$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
4550.2.a.cb	$4550$	$2$	4550.a	1.a	$1$	$5$	$5$	$36.332$	5.5.18285500.1	None	✓	$1$	$0$	\(-5\)	\(-2\)	\(0\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
4550.2.a.cc	$4550$	$2$	4550.a	1.a	$1$	$5$	$5$	$36.332$	5.5.18285500.1	None	✓	$1$	$0$	\(5\)	\(2\)	\(0\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)
4550.2.a.cd	$4550$	$2$	4550.a	1.a	$1$	$5$	$5$	$36.332$	5.5.117688.1	None	✓	$1$	$0$	\(5\)	\(4\)	\(0\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2275))\)\(^{\oplus 2}\)