Space of modular forms of level 4650, weight 2, and trivial character

• Label: 4650.2.a
• Level: $4650$
• Weight: $2$
• Character orbit: 4650.a
• Rep. character: $\chi_{4650}(1,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $68$
• Sturm bound: $1920$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 68 \)
Sturm bound:			\(1920\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4650))\).

	Total	New	Old
Modular forms	984	94	890
Cusp forms	937	94	843
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.

\(2\)	\(3\)	\(5\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(4\)
Plus space				\(+\)	\(38\)
Minus space				\(-\)	\(56\)

Trace form

\( 94 q - 2 q^{2} + 94 q^{4} - 8 q^{7} - 2 q^{8} + 94 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4650))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	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	5	31
4650.2.a.a	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots\)
4650.2.a.b	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.c	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.e	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.d	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.n	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.e	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.f	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.g	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.g	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.h	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.o	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.i	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				186.2.a.c	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.j	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.f	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.k	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.k	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.l	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.l	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.m	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.c	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(5\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
4650.2.a.n	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.m	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.o	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.o	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.p	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.q	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.q	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.r	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.l	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.s	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.s	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
4650.2.a.t	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.k	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.u	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.d	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.v	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.v	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.w	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.x	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.j	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.y	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.v	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.z	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.d	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.ba	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.s	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bb	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.f	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bc	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bd	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.i	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.be	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.o	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bf	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.q	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bg	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.h	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bh	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				186.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bi	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.c	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
4650.2.a.bj	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.l	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bk	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.e	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bl	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.d	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bm	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.f	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bn	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.k	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bo	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				186.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bp	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.b	$1$	$1$	\(1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
4650.2.a.bq	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.b	$1$	$1$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.br	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.g	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bs	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.d.e	$1$	$0$	\(1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bt	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.e	$1$	$0$	\(1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bu	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.b	$1$	$0$	\(1\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bv	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bw	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓				930.2.a.c	$1$	$0$	\(1\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4650.2.a.bx	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	\(\Q\)	None	✓	✓			4650.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+5q^{7}+q^{8}+\cdots\)
4650.2.a.by	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{33}) \)	None	✓		✓		930.2.a.r	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.bz	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{65}) \)	None	✓				930.2.a.q	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ca	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{5}) \)	None	✓	✓			4650.2.a.ca	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cb	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{13}) \)	None	✓	✓			4650.2.a.cb	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(6\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.cc	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{2}) \)	None	✓				930.2.d.g	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
4650.2.a.cd	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{17}) \)	None	✓		✓		186.2.a.d	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-2\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ce	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{17}) \)	None	✓				930.2.a.p	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.cf	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{2}) \)	None	✓				930.2.d.g	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cg	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓		4650.2.a.cb	$1$	$1$	\(2\)	\(2\)	\(0\)	\(-6\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.ch	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		4650.2.a.ca	$1$	$1$	\(2\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+(-2-\beta )q^{7}+\cdots\)
4650.2.a.ci	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1708.1	None	✓		✓		930.2.d.i	$1$	$0$	\(-3\)	\(-3\)	\(0\)	\(-6\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.cj	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.837.1	None	✓	✓	✓		4650.2.a.cj	$1$	$1$	\(-3\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{2}q^{7}-q^{8}+\cdots\)
4650.2.a.ck	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.940.1	None	✓		✓		930.2.d.h	$1$	$0$	\(-3\)	\(3\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4650.2.a.cl	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1373.1	None	✓	✓	✓		4650.2.a.cl	$1$	$1$	\(-3\)	\(3\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(1-\beta _{2})q^{7}+\cdots\)
4650.2.a.cm	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1373.1	None	✓	✓			4650.2.a.cl	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{2})q^{7}+\cdots\)
4650.2.a.cn	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.940.1	None	✓				930.2.d.h	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(-1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4650.2.a.co	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.837.1	None	✓	✓	✓		4650.2.a.cj	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{2}q^{7}+q^{8}+\cdots\)
4650.2.a.cp	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1708.1	None	✓		✓		930.2.d.i	$1$	$0$	\(3\)	\(3\)	\(0\)	\(6\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4650)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(775))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2325))\)\(^{\oplus 2}\)