Space of modular forms of level 6600, weight 2, and trivial character

• Label: 6600.2.a
• Level: $6600$
• Weight: $2$
• Character orbit: 6600.a
• Rep. character: $\chi_{6600}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $53$
• Sturm bound: $2880$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6600 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6600.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 53 \)
Sturm bound:			\(2880\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6600))\).

	Total	New	Old
Modular forms	1488	96	1392
Cusp forms	1393	96	1297
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(5\)
Plus space				\(+\)	\(42\)
Minus space				\(-\)	\(54\)

Trace form

\( 96 q + 2 q^{3} + 4 q^{7} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6600))\) 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	5	11
6600.2.a.a	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
6600.2.a.b	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
6600.2.a.c	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
6600.2.a.d	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+q^{11}-4q^{17}+\cdots\)
6600.2.a.e	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+q^{11}+2q^{17}+\cdots\)
6600.2.a.f	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
6600.2.a.g	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6600.2.a.h	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+q^{11}-q^{13}-2q^{17}+\cdots\)
6600.2.a.i	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}+3q^{17}+\cdots\)
6600.2.a.j	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}-4q^{17}+\cdots\)
6600.2.a.k	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}+6q^{17}+\cdots\)
6600.2.a.l	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}+q^{13}-4q^{17}+\cdots\)
6600.2.a.m	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
6600.2.a.n	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+q^{11}+8q^{17}+\cdots\)
6600.2.a.o	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}+q^{11}-3q^{17}+\cdots\)
6600.2.a.p	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
6600.2.a.q	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
6600.2.a.r	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
6600.2.a.s	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}+q^{11}+3q^{17}+\cdots\)
6600.2.a.t	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-q^{11}-q^{13}+4q^{17}+\cdots\)
6600.2.a.u	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
6600.2.a.v	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-3q^{17}+\cdots\)
6600.2.a.w	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+q^{11}+q^{13}+2q^{17}+\cdots\)
6600.2.a.x	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-q^{11}+2q^{13}+6q^{17}+\cdots\)
6600.2.a.y	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+q^{11}-2q^{13}-6q^{17}+\cdots\)
6600.2.a.z	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+q^{11}+6q^{13}+6q^{17}+\cdots\)
6600.2.a.ba	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-q^{11}+q^{17}+q^{19}+\cdots\)
6600.2.a.bb	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
6600.2.a.bc	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
6600.2.a.bd	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
6600.2.a.be	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-q^{11}+5q^{13}+\cdots\)
6600.2.a.bf	$6600$	$2$	6600.a	1.a	$1$	$1$	$1$	$52.701$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
6600.2.a.bg	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-5\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{7}+q^{9}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
6600.2.a.bh	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{7}+q^{9}+q^{11}+(-2-\beta )q^{13}+\cdots\)
6600.2.a.bi	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+q^{11}-2\beta q^{13}+\cdots\)
6600.2.a.bj	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+q^{11}-2\beta q^{13}+\cdots\)
6600.2.a.bk	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{7}+q^{9}-q^{11}+(-2-\beta )q^{13}+\cdots\)
6600.2.a.bl	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
6600.2.a.bm	$6600$	$2$	6600.a	1.a	$1$	$2$	$2$	$52.701$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(3-\beta )q^{7}+q^{9}+q^{11}+(1+2\beta )q^{13}+\cdots\)
6600.2.a.bn	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.2024.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{7}+q^{9}+q^{11}+\cdots\)
6600.2.a.bo	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.1304.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{7}+q^{9}-q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
6600.2.a.bp	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
6600.2.a.bq	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2})q^{7}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)
6600.2.a.br	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.9192.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
6600.2.a.bs	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.9192.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{7}+q^{9}-q^{11}+\cdots\)
6600.2.a.bt	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}-q^{11}+\cdots\)
6600.2.a.bu	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{2})q^{7}+q^{9}+q^{11}+\cdots\)
6600.2.a.bv	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.1304.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{7}+q^{9}-q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots\)
6600.2.a.bw	$6600$	$2$	6600.a	1.a	$1$	$3$	$3$	$52.701$	3.3.2024.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{7}+q^{9}+q^{11}+\beta _{2}q^{13}+\cdots\)
6600.2.a.bx	$6600$	$2$	6600.a	1.a	$1$	$5$	$5$	$52.701$	5.5.2389280.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{7}+q^{9}-q^{11}+(-\beta _{3}+\cdots)q^{13}+\cdots\)
6600.2.a.by	$6600$	$2$	6600.a	1.a	$1$	$5$	$5$	$52.701$	5.5.1633440.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{7}+q^{9}+q^{11}+(-2-\beta _{1}+\cdots)q^{13}+\cdots\)
6600.2.a.bz	$6600$	$2$	6600.a	1.a	$1$	$5$	$5$	$52.701$	5.5.2389280.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{7}+q^{9}-q^{11}+(\beta _{3}+\beta _{4})q^{13}+\cdots\)
6600.2.a.ca	$6600$	$2$	6600.a	1.a	$1$	$5$	$5$	$52.701$	5.5.1633440.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(0\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{7}+q^{9}+q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3300))\)\(^{\oplus 2}\)