Space of modular forms of level 7245, weight 2, and trivial character

• Label: 7245.2.a
• Level: $7245$
• Weight: $2$
• Character orbit: 7245.a
• Rep. character: $\chi_{7245}(1,\cdot)$
• Character field: $\Q$
• Dimension: $220$
• Newform subspaces: $52$
• Sturm bound: $2304$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7245.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(2304\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7245))\).

	Total	New	Old
Modular forms	1168	220	948
Cusp forms	1137	220	917
Eisenstein series	31	0	31

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

\(3\)	\(5\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(13\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(13\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(9\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(9\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(13\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(18\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(17\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(18\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(17\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(13\)
Plus space				\(+\)	\(98\)
Minus space				\(-\)	\(122\)

Trace form

\( 220 q - 4 q^{2} + 220 q^{4} - 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7245))\) 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	5	7	23
7245.2.a.a	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.b	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.c	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.d	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.e	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7245.2.a.f	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7245.2.a.g	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7245.2.a.h	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-q^{10}+\cdots\)
7245.2.a.i	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-q^{7}-q^{11}+4q^{16}+\cdots\)
7245.2.a.j	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}-3q^{11}-4q^{13}+\cdots\)
7245.2.a.k	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots\)
7245.2.a.l	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
7245.2.a.m	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
7245.2.a.n	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.o	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.p	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.q	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.r	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.s	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}+q^{10}+\cdots\)
7245.2.a.t	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.u	$7245$	$2$	7245.a	1.a	$1$	$1$	$1$	$57.852$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7245.2.a.v	$7245$	$2$	7245.a	1.a	$1$	$2$	$2$	$57.852$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots\)
7245.2.a.w	$7245$	$2$	7245.a	1.a	$1$	$2$	$2$	$57.852$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}-q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
7245.2.a.x	$7245$	$2$	7245.a	1.a	$1$	$2$	$2$	$57.852$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}+q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
7245.2.a.y	$7245$	$2$	7245.a	1.a	$1$	$3$	$3$	$57.852$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-q^{7}+\cdots\)
7245.2.a.z	$7245$	$2$	7245.a	1.a	$1$	$3$	$3$	$57.852$	3.3.148.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+q^{7}+\cdots\)
7245.2.a.ba	$7245$	$2$	7245.a	1.a	$1$	$3$	$3$	$57.852$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7245.2.a.bb	$7245$	$2$	7245.a	1.a	$1$	$3$	$3$	$57.852$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7245.2.a.bc	$7245$	$2$	7245.a	1.a	$1$	$4$	$4$	$57.852$	4.4.2777.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7245.2.a.bd	$7245$	$2$	7245.a	1.a	$1$	$4$	$4$	$57.852$	4.4.7537.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}-\beta _{3}q^{8}+\cdots\)
7245.2.a.be	$7245$	$2$	7245.a	1.a	$1$	$4$	$4$	$57.852$	4.4.22545.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
7245.2.a.bf	$7245$	$2$	7245.a	1.a	$1$	$4$	$4$	$57.852$	4.4.2777.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(1-\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
7245.2.a.bg	$7245$	$2$	7245.a	1.a	$1$	$5$	$5$	$57.852$	5.5.2508628.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7245.2.a.bh	$7245$	$2$	7245.a	1.a	$1$	$5$	$5$	$57.852$	5.5.255877.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(5\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots\)
7245.2.a.bi	$7245$	$2$	7245.a	1.a	$1$	$5$	$5$	$57.852$	5.5.122821.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(-5\)	\(-5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(\beta _{3}+\beta _{4})q^{4}-q^{5}-q^{7}+\cdots\)
7245.2.a.bj	$7245$	$2$	7245.a	1.a	$1$	$6$	$6$	$57.852$	6.6.15751800.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(6\)	\(6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+q^{7}+\cdots\)
7245.2.a.bk	$7245$	$2$	7245.a	1.a	$1$	$6$	$6$	$57.852$	6.6.42978136.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(6\)	\(-6\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bl	$7245$	$2$	7245.a	1.a	$1$	$7$	$7$	$57.852$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(7\)	\(7\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bm	$7245$	$2$	7245.a	1.a	$1$	$7$	$7$	$57.852$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-7\)	\(-7\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bn	$7245$	$2$	7245.a	1.a	$1$	$7$	$7$	$57.852$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(7\)	\(-7\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7245.2.a.bo	$7245$	$2$	7245.a	1.a	$1$	$8$	$8$	$57.852$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(8\)	\(-8\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-q^{7}+\cdots\)
7245.2.a.bp	$7245$	$2$	7245.a	1.a	$1$	$8$	$8$	$57.852$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-8\)	\(8\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bq	$7245$	$2$	7245.a	1.a	$1$	$8$	$8$	$57.852$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-8\)	\(-8\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-q^{7}+\cdots\)
7245.2.a.br	$7245$	$2$	7245.a	1.a	$1$	$9$	$9$	$57.852$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(9\)	\(9\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}-\beta _{3}q^{8}+\cdots\)
7245.2.a.bs	$7245$	$2$	7245.a	1.a	$1$	$9$	$9$	$57.852$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-9\)	\(9\)		$-$	$+$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bt	$7245$	$2$	7245.a	1.a	$1$	$9$	$9$	$57.852$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-9\)	\(9\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+\beta _{3}q^{8}+\cdots\)
7245.2.a.bu	$7245$	$2$	7245.a	1.a	$1$	$10$	$10$	$57.852$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-10\)	\(-10\)		$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}-q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bv	$7245$	$2$	7245.a	1.a	$1$	$10$	$10$	$57.852$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-10\)	\(10\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots\)
7245.2.a.bw	$7245$	$2$	7245.a	1.a	$1$	$10$	$10$	$57.852$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-10\)	\(-10\)		$+$	$+$	$+$	$-$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
7245.2.a.bx	$7245$	$2$	7245.a	1.a	$1$	$10$	$10$	$57.852$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(10\)	\(-10\)		$+$	$-$	$+$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7245.2.a.by	$7245$	$2$	7245.a	1.a	$1$	$13$	$13$	$57.852$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-13\)	\(13\)		$+$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7245.2.a.bz	$7245$	$2$	7245.a	1.a	$1$	$13$	$13$	$57.852$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(13\)	\(13\)		$+$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7245))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7245)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2415))\)\(^{\oplus 2}\)