Space of modular forms of level 7225, weight 2, and trivial character

• Label: 7225.2.a
• Level: $7225$
• Weight: $2$
• Character orbit: 7225.a
• Rep. character: $\chi_{7225}(1,\cdot)$
• Character field: $\Q$
• Dimension: $406$
• Newform subspaces: $54$
• Sturm bound: $1530$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 54 \)
Sturm bound:			\(1530\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7225))\).

	Total	New	Old
Modular forms	818	451	367
Cusp forms	711	406	305
Eisenstein series	107	45	62

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

\(5\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(96\)
\(+\)	\(-\)	$-$	\(100\)
\(-\)	\(+\)	$-$	\(109\)
\(-\)	\(-\)	$+$	\(101\)
Plus space		\(+\)	\(197\)
Minus space		\(-\)	\(209\)

Trace form

\( 406 q - 2 q^{2} + 378 q^{4} - 4 q^{7} - 6 q^{8} + 362 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7225))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	17
7225.2.a.a	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}-5q^{7}+3q^{8}+\cdots\)
7225.2.a.b	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
7225.2.a.c	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+5q^{7}+3q^{8}+\cdots\)
7225.2.a.d	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots\)
7225.2.a.e	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+2q^{7}+q^{9}+3q^{11}+\cdots\)
7225.2.a.f	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-2q^{7}+q^{9}-3q^{11}+\cdots\)
7225.2.a.g	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{9}+2q^{13}+\cdots\)
7225.2.a.h	$7225$	$2$	7225.a	1.a	$1$	$1$	$1$	$57.692$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
7225.2.a.i	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}-q^{4}+\beta q^{6}+3\beta q^{7}+\cdots\)
7225.2.a.j	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-\beta q^{3}+(2+\beta )q^{4}+(4+\beta )q^{6}+\cdots\)
7225.2.a.k	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+\beta q^{3}+(2+\beta )q^{4}+(-4-\beta )q^{6}+\cdots\)
7225.2.a.l	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+(3+\beta )q^{6}+\cdots\)
7225.2.a.m	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots\)
7225.2.a.n	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(1\)	\(1\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots\)
7225.2.a.o	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(-4\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-2+\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
7225.2.a.p	$7225$	$2$	7225.a	1.a	$1$	$2$	$2$	$57.692$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}-q^{4}+\beta q^{6}-3\beta q^{7}+\cdots\)
7225.2.a.q	$7225$	$2$	7225.a	1.a	$1$	$3$	$3$	$57.692$	3.3.148.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
7225.2.a.r	$7225$	$2$	7225.a	1.a	$1$	$3$	$3$	$57.692$	3.3.148.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
7225.2.a.s	$7225$	$2$	7225.a	1.a	$1$	$3$	$3$	$57.692$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
7225.2.a.t	$7225$	$2$	7225.a	1.a	$1$	$3$	$3$	$57.692$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(1+2\beta _{1}+\cdots)q^{6}+\cdots\)
7225.2.a.u	$7225$	$2$	7225.a	1.a	$1$	$4$	$4$	$57.692$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
7225.2.a.v	$7225$	$2$	7225.a	1.a	$1$	$4$	$4$	$57.692$	4.4.6224.1	None	✓	$1$	$0$	\(-2\)	\(4\)	\(0\)	\(10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
7225.2.a.w	$7225$	$2$	7225.a	1.a	$1$	$4$	$4$	$57.692$	4.4.6224.1	None	✓	$1$	$0$	\(2\)	\(-4\)	\(0\)	\(-10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
7225.2.a.x	$7225$	$2$	7225.a	1.a	$1$	$5$	$5$	$57.692$	5.5.1893456.1	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
7225.2.a.y	$7225$	$2$	7225.a	1.a	$1$	$5$	$5$	$57.692$	5.5.1893456.1	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
7225.2.a.z	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.7718912.1	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
7225.2.a.ba	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.93924352.2	None	✓	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)
7225.2.a.bb	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.7718912.1	None	✓	$1$	$1$	\(-2\)	\(4\)	\(0\)	\(8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
7225.2.a.bc	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.199789929.1	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
7225.2.a.bd	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.199789929.1	None	✓	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
7225.2.a.be	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.199789929.1	None	✓	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
7225.2.a.bf	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.199789929.1	None	✓	$1$	$0$	\(1\)	\(2\)	\(0\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
7225.2.a.bg	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.93924352.2	None	✓	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)
7225.2.a.bh	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.1397493.1	None	✓	$1$	$1$	\(3\)	\(-3\)	\(0\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
7225.2.a.bi	$7225$	$2$	7225.a	1.a	$1$	$6$	$6$	$57.692$	6.6.1397493.1	None	✓	$1$	$0$	\(3\)	\(3\)	\(0\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
7225.2.a.bj	$7225$	$2$	7225.a	1.a	$1$	$8$	$8$	$57.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
7225.2.a.bk	$7225$	$2$	7225.a	1.a	$1$	$8$	$8$	$57.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{6}+\cdots\)
7225.2.a.bl	$7225$	$2$	7225.a	1.a	$1$	$8$	$8$	$57.692$	8.8.\(\cdots\).1	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2-\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
7225.2.a.bm	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{8}q^{2}+\beta _{1}q^{3}+(1+\beta _{4})q^{4}-\beta _{11}q^{6}+\cdots\)
7225.2.a.bn	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(0\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
7225.2.a.bo	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(3\)	\(0\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{2})q^{4}+(1-2\beta _{1}+\cdots)q^{6}+\cdots\)
7225.2.a.bp	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}-\beta _{9}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
7225.2.a.bq	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(-8\)	\(0\)	\(-16\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7225.2.a.br	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{8}q^{2}+\beta _{1}q^{3}+(1+\beta _{4})q^{4}+\beta _{11}q^{6}+\cdots\)
7225.2.a.bs	$7225$	$2$	7225.a	1.a	$1$	$12$	$12$	$57.692$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(8\)	\(0\)	\(16\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7225.2.a.bt	$7225$	$2$	7225.a	1.a	$1$	$15$	$15$	$57.692$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(0\)	\(-12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{12})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
7225.2.a.bu	$7225$	$2$	7225.a	1.a	$1$	$15$	$15$	$57.692$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(0\)	\(-12\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{12})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
7225.2.a.bv	$7225$	$2$	7225.a	1.a	$1$	$15$	$15$	$57.692$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(0\)	\(12\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{12})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
7225.2.a.bw	$7225$	$2$	7225.a	1.a	$1$	$15$	$15$	$57.692$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(0\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{12})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
7225.2.a.bx	$7225$	$2$	7225.a	1.a	$1$	$24$	$24$	$57.692$		None	✓	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7225.2.a.by	$7225$	$2$	7225.a	1.a	$1$	$24$	$24$	$57.692$		None	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7225.2.a.bz	$7225$	$2$	7225.a	1.a	$1$	$24$	$24$	$57.692$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7225.2.a.ca	$7225$	$2$	7225.a	1.a	$1$	$24$	$24$	$57.692$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
7225.2.a.cb	$7225$	$2$	7225.a	1.a	$1$	$24$	$24$	$57.692$		None	✓	$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 2}\)