Space of modular forms of level 6552, weight 2, and trivial character

• Label: 6552.2.a
• Level: $6552$
• Weight: $2$
• Character orbit: 6552.a
• Rep. character: $\chi_{6552}(1,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $49$
• Sturm bound: $2688$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6552 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6552.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6552))\).

	Total	New	Old
Modular forms	1376	90	1286
Cusp forms	1313	90	1223
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.

\(2\)	\(3\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(5\)
Plus space				\(+\)	\(42\)
Minus space				\(-\)	\(48\)

Trace form

\( 90 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6552))\) 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	7	13
6552.2.a.a	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.h	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}-6q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.b	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots\)
6552.2.a.c	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				728.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}-q^{13}+2q^{17}+5q^{19}+\cdots\)
6552.2.a.d	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
6552.2.a.e	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+q^{13}+6q^{17}-4q^{19}+\cdots\)
6552.2.a.f	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.g	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots\)
6552.2.a.h	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
6552.2.a.i	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-q^{11}+q^{13}+3q^{17}+\cdots\)
6552.2.a.j	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
6552.2.a.k	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-2q^{11}-q^{13}+2q^{17}-5q^{25}+\cdots\)
6552.2.a.l	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+2q^{11}-q^{13}+2q^{17}+8q^{23}+\cdots\)
6552.2.a.m	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				728.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{11}-q^{13}-4q^{17}+2q^{19}+\cdots\)
6552.2.a.n	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.n	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-q^{13}-2q^{17}-4q^{19}-2q^{23}+\cdots\)
6552.2.a.o	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.n	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-q^{13}+2q^{17}-4q^{19}+2q^{23}+\cdots\)
6552.2.a.p	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.l	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+2q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots\)
6552.2.a.q	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				728.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}+q^{13}-7q^{19}+\cdots\)
6552.2.a.r	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.i	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+q^{11}+q^{13}-3q^{17}+\cdots\)
6552.2.a.s	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				728.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots\)
6552.2.a.t	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.g	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.u	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.j	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
6552.2.a.v	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots\)
6552.2.a.w	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-6q^{11}-q^{13}+8q^{17}+\cdots\)
6552.2.a.x	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
6552.2.a.y	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.i	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+2q^{11}-q^{13}+7q^{19}+\cdots\)
6552.2.a.z	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓				2184.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots\)
6552.2.a.ba	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	\(\Q\)	None	✓	✓			6552.2.a.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots\)
6552.2.a.bb	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{33}) \)	None	✓	✓			6552.2.a.bb	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+\cdots\)
6552.2.a.bc	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		6552.2.a.bc	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+\cdots\)
6552.2.a.bd	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{33}) \)	None	✓				2184.2.a.r	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
6552.2.a.be	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{17}) \)	None	✓				2184.2.a.p	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+q^{7}+2q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
6552.2.a.bf	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{3}) \)	None	✓				728.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(1-\beta )q^{11}-q^{13}+(-1+\cdots)q^{17}+\cdots\)
6552.2.a.bg	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{17}) \)	None	✓				728.2.a.g	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bh	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{17}) \)	None	✓				2184.2.a.o	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
6552.2.a.bi	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		6552.2.a.bc	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(1+\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bj	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{2}) \)	None	✓				728.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+(2-3\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bk	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{17}) \)	None	✓				2184.2.a.n	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bl	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{17}) \)	None	✓				2184.2.a.q	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bm	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	\(\Q(\sqrt{33}) \)	None	✓	✓			6552.2.a.bb	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(3-\beta )q^{11}-q^{13}+\cdots\)
6552.2.a.bn	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.316.1	None	✓		✓		2184.2.a.u	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6552.2.a.bo	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.961.1	None	✓		✓		2184.2.a.t	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}+(-3+\beta _{1}-\beta _{2})q^{11}+\cdots\)
6552.2.a.bp	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.2089.1	None	✓		✓		2184.2.a.s	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{11}-q^{13}+\cdots\)
6552.2.a.bq	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.19664.1	None	✓	✓	✓		6552.2.a.bq	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}-q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6552.2.a.br	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.64268.1	None	✓		✓		728.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}-q^{7}+(\beta _{1}+2\beta _{3})q^{11}+\cdots\)
6552.2.a.bs	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.138892.1	None	✓		✓		2184.2.a.v	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}-q^{7}+(1-\beta _{2})q^{11}+\cdots\)
6552.2.a.bt	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.183064.1	None	✓		✓		728.2.a.h	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+q^{7}-\beta _{1}q^{11}+q^{13}+(-1+\cdots)q^{17}+\cdots\)
6552.2.a.bu	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.19664.1	None	✓	✓	✓		6552.2.a.bq	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}-q^{7}+(1+\beta _{1})q^{11}-q^{13}+\cdots\)
6552.2.a.bv	$6552$	$2$	6552.a	1.a	$1$	$5$	$5$	$52.318$	5.5.9654428.1	None	✓	✓	✓		6552.2.a.bv	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(5\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+q^{7}+(-2-\beta _{3})q^{11}+q^{13}+\cdots\)
6552.2.a.bw	$6552$	$2$	6552.a	1.a	$1$	$5$	$5$	$52.318$	5.5.9654428.1	None	✓	✓	✓		6552.2.a.bv	$1$	$0$	\(0\)	\(0\)	\(1\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(2+\beta _{3})q^{11}+q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6552)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(819))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1638))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3276))\)\(^{\oplus 2}\)