Space of modular forms of level 7497, weight 2, and trivial character

• Label: 7497.2.a
• Level: $7497$
• Weight: $2$
• Character orbit: 7497.a
• Rep. character: $\chi_{7497}(1,\cdot)$
• Character field: $\Q$
• Dimension: $274$
• Newform subspaces: $65$
• Sturm bound: $2016$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7497 = 3^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7497.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 65 \)
Sturm bound:			\(2016\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7497))\).

	Total	New	Old
Modular forms	1040	274	766
Cusp forms	977	274	703
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.

\(3\)	\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(27\)
\(+\)	\(+\)	\(-\)	$-$	\(27\)
\(+\)	\(-\)	\(+\)	$-$	\(28\)
\(+\)	\(-\)	\(-\)	$+$	\(28\)
\(-\)	\(+\)	\(+\)	$-$	\(42\)
\(-\)	\(+\)	\(-\)	$+$	\(38\)
\(-\)	\(-\)	\(+\)	$+$	\(39\)
\(-\)	\(-\)	\(-\)	$-$	\(45\)
Plus space			\(+\)	\(132\)
Minus space			\(-\)	\(142\)

Trace form

\( 274 q - 2 q^{2} + 274 q^{4} - 18 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7497))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	17
7497.2.a.a	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-3q^{11}+\cdots\)
7497.2.a.b	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-q^{11}+\cdots\)
7497.2.a.c	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-3q^{5}+3q^{8}+3q^{10}+\cdots\)
7497.2.a.d	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
7497.2.a.e	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
7497.2.a.f	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{5}+3q^{8}-3q^{10}+\cdots\)
7497.2.a.g	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}-4q^{11}+q^{13}+4q^{16}+\cdots\)
7497.2.a.h	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-3q^{11}-3q^{13}+4q^{16}+\cdots\)
7497.2.a.i	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+5q^{11}+5q^{13}+4q^{16}+\cdots\)
7497.2.a.j	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}+3q^{11}+q^{13}+4q^{16}+\cdots\)
7497.2.a.k	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{5}-4q^{11}-q^{13}+4q^{16}+\cdots\)
7497.2.a.l	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
7497.2.a.m	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+2q^{11}+\cdots\)
7497.2.a.n	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots\)
7497.2.a.o	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+3q^{11}+\cdots\)
7497.2.a.p	$7497$	$2$	7497.a	1.a	$1$	$1$	$1$	$59.864$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+3q^{11}+\cdots\)
7497.2.a.q	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
7497.2.a.r	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
7497.2.a.s	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{5}-2\beta q^{8}+(2-\beta )q^{10}+\cdots\)
7497.2.a.t	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{5}-2\beta q^{8}+(2-\beta )q^{10}+\cdots\)
7497.2.a.u	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{5}-2\beta q^{8}+(-2+\beta )q^{10}+\cdots\)
7497.2.a.v	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(4+\beta )q^{8}+\cdots\)
7497.2.a.w	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
7497.2.a.x	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
7497.2.a.y	$7497$	$2$	7497.a	1.a	$1$	$2$	$2$	$59.864$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
7497.2.a.z	$7497$	$2$	7497.a	1.a	$1$	$3$	$3$	$59.864$	3.3.148.1	None	✓	$1$	$0$	\(-2\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7497.2.a.ba	$7497$	$2$	7497.a	1.a	$1$	$3$	$3$	$59.864$	3.3.316.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
7497.2.a.bb	$7497$	$2$	7497.a	1.a	$1$	$3$	$3$	$59.864$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1})q^{5}+(1+\cdots)q^{8}+\cdots\)
7497.2.a.bc	$7497$	$2$	7497.a	1.a	$1$	$3$	$3$	$59.864$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bd	$7497$	$2$	7497.a	1.a	$1$	$3$	$3$	$59.864$	3.3.148.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(-5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
7497.2.a.be	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.7232.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{2}-\beta _{3})q^{4}+\beta _{1}q^{5}+\cdots\)
7497.2.a.bf	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	\(\Q(\sqrt{2}, \sqrt{39})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{5}+2\beta _{2}q^{8}+\beta _{2}q^{10}+\cdots\)
7497.2.a.bg	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	\(\Q(\zeta_{16})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bh	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	\(\Q(\sqrt{2}, \sqrt{39})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{5}+2\beta _{2}q^{8}-\beta _{2}q^{10}+\cdots\)
7497.2.a.bi	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	\(\Q(\zeta_{16})^+\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bj	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.1957.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
7497.2.a.bk	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.1957.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bl	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.9301.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
7497.2.a.bm	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.14013.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7497.2.a.bn	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.14013.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
7497.2.a.bo	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.9301.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
7497.2.a.bp	$7497$	$2$	7497.a	1.a	$1$	$4$	$4$	$59.864$	4.4.9301.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
7497.2.a.bq	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.1224176.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
7497.2.a.br	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.453749.1	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bs	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.885424.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
7497.2.a.bt	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.885424.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
7497.2.a.bu	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.1224176.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
7497.2.a.bv	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.1383597.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bw	$7497$	$2$	7497.a	1.a	$1$	$5$	$5$	$59.864$	5.5.1383597.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bx	$7497$	$2$	7497.a	1.a	$1$	$6$	$6$	$59.864$	6.6.29722117.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-7\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7497.2.a.by	$7497$	$2$	7497.a	1.a	$1$	$6$	$6$	$59.864$	6.6.29722117.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(7\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
7497.2.a.bz	$7497$	$2$	7497.a	1.a	$1$	$7$	$7$	$59.864$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\beta _{3}q^{5}+\cdots\)
7497.2.a.ca	$7497$	$2$	7497.a	1.a	$1$	$7$	$7$	$59.864$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
7497.2.a.cb	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	8.8.\(\cdots\).1	None	✓	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
7497.2.a.cc	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	8.8.\(\cdots\).1	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{6})q^{5}+\cdots\)
7497.2.a.cd	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	8.8.\(\cdots\).1	None	✓	$2$	$1$	\(0\)	\(0\)	\(-12\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(-2+\beta _{3}+\cdots)q^{5}+\cdots\)
7497.2.a.ce	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	8.8.\(\cdots\).1	None	✓	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots\)
7497.2.a.cf	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
7497.2.a.cg	$7497$	$2$	7497.a	1.a	$1$	$8$	$8$	$59.864$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
7497.2.a.ch	$7497$	$2$	7497.a	1.a	$1$	$11$	$11$	$59.864$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
7497.2.a.ci	$7497$	$2$	7497.a	1.a	$1$	$11$	$11$	$59.864$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
7497.2.a.cj	$7497$	$2$	7497.a	1.a	$1$	$11$	$11$	$59.864$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
7497.2.a.ck	$7497$	$2$	7497.a	1.a	$1$	$11$	$11$	$59.864$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
7497.2.a.cl	$7497$	$2$	7497.a	1.a	$1$	$12$	$12$	$59.864$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{7}q^{5}+(-2+\cdots)q^{8}+\cdots\)
7497.2.a.cm	$7497$	$2$	7497.a	1.a	$1$	$12$	$12$	$59.864$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+(-2+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7497))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7497)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1071))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2499))\)\(^{\oplus 2}\)