Space of modular forms of level 6272, weight 2, and trivial character

• Label: 6272.2.a
• Level: $6272$
• Weight: $2$
• Character orbit: 6272.a
• Rep. character: $\chi_{6272}(1,\cdot)$
• Character field: $\Q$
• Dimension: $164$
• Newform subspaces: $52$
• Sturm bound: $1792$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 6272 = 2^{7} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6272.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1792\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6272))\).

	Total	New	Old
Modular forms	960	164	796
Cusp forms	833	164	669
Eisenstein series	127	0	127

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

\(2\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(36\)
\(+\)	\(-\)	\(-\)	\(45\)
\(-\)	\(+\)	\(-\)	\(44\)
\(-\)	\(-\)	\(+\)	\(39\)
Plus space		\(+\)	\(75\)
Minus space		\(-\)	\(89\)

Trace form

\( 164 q + 164 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6272))\) 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	7
6272.2.a.a	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
6272.2.a.b	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6272.2.a.c	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.d	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}-2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.e	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}+2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.f	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}+2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.g	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
6272.2.a.h	$6272$	$2$	6272.a	1.a	$1$	$1$	$1$	$50.082$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6272.2.a.i	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.j	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.k	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}-q^{9}-4q^{11}-4q^{15}+\cdots\)
6272.2.a.l	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+4q^{15}+\cdots\)
6272.2.a.m	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.n	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.o	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.p	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.q	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}-q^{9}+4q^{11}-4q^{15}+\cdots\)
6272.2.a.r	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}+4q^{11}+4q^{15}+\cdots\)
6272.2.a.s	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.t	$6272$	$2$	6272.a	1.a	$1$	$2$	$2$	$50.082$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.u	$6272$	$2$	6272.a	1.a	$1$	$3$	$3$	$50.082$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots\)
6272.2.a.v	$6272$	$2$	6272.a	1.a	$1$	$3$	$3$	$50.082$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.w	$6272$	$2$	6272.a	1.a	$1$	$3$	$3$	$50.082$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.x	$6272$	$2$	6272.a	1.a	$1$	$3$	$3$	$50.082$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.y	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.z	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.ba	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bb	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bc	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bd	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.be	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bf	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bg	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bh	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bi	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bj	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(1+\cdots)q^{11}+\cdots\)
6272.2.a.bk	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.9248.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bl	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.9248.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bm	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.9248.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bn	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.9248.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bo	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bp	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bq	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.br	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bs	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bt	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bu	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.11344.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bv	$6272$	$2$	6272.a	1.a	$1$	$4$	$4$	$50.082$	4.4.54864.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bw	$6272$	$2$	6272.a	1.a	$1$	$6$	$6$	$50.082$	6.6.26849792.2	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bx	$6272$	$2$	6272.a	1.a	$1$	$6$	$6$	$50.082$	6.6.26849792.2	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)
6272.2.a.by	$6272$	$2$	6272.a	1.a	$1$	$6$	$6$	$50.082$	6.6.26849792.2	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bz	$6272$	$2$	6272.a	1.a	$1$	$6$	$6$	$50.082$	6.6.26849792.2	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6272))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 2}\)