Space of modular forms of level 9025, weight 2, and trivial character

• Label: 9025.2.a
• Level: $9025$
• Weight: $2$
• Character orbit: 9025.a
• Rep. character: $\chi_{9025}(1,\cdot)$
• Character field: $\Q$
• Dimension: $515$
• Newform subspaces: $74$
• Sturm bound: $1900$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 74 \)
Sturm bound:			\(1900\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9025))\).

	Total	New	Old
Modular forms	1010	566	444
Cusp forms	891	515	376
Eisenstein series	119	51	68

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

\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(245\)	\(129\)	\(116\)		\(216\)	\(121\)	\(95\)		\(29\)	\(8\)	\(21\)
\(+\)	\(-\)	\(-\)		\(260\)	\(135\)	\(125\)		\(230\)	\(126\)	\(104\)		\(30\)	\(9\)	\(21\)
\(-\)	\(+\)	\(-\)		\(255\)	\(155\)	\(100\)		\(225\)	\(139\)	\(86\)		\(30\)	\(16\)	\(14\)
\(-\)	\(-\)	\(+\)		\(250\)	\(147\)	\(103\)		\(220\)	\(129\)	\(91\)		\(30\)	\(18\)	\(12\)
Plus space		\(+\)		\(495\)	\(276\)	\(219\)		\(436\)	\(250\)	\(186\)		\(59\)	\(26\)	\(33\)
Minus space		\(-\)		\(515\)	\(290\)	\(225\)		\(455\)	\(265\)	\(190\)		\(60\)	\(25\)	\(35\)

Trace form

515 * q - q^2 + 2 * q^3 + 487 * q^4 + 2 * q^7 - 9 * q^8 + 473 * q^9 + 2 * q^11 + 6 * q^13 + 439 * q^16 + 2 * q^17 - 29 * q^18 + 6 * q^21 - 12 * q^22 - 16 * q^23 - 16 * q^24 - 14 * q^26 + 8 * q^27 + 2 * q^28 + 16 * q^31 - 9 * q^32 + 6 * q^33 + 10 * q^34 + 427 * q^36 + 16 * q^37 + 52 * q^39 - 4 * q^41 + 58 * q^42 - 6 * q^43 - 10 * q^44 - 4 * q^46 - 10 * q^47 + 40 * q^48 + 389 * q^49 + 2 * q^51 + 30 * q^52 + 18 * q^53 + 50 * q^54 + 32 * q^56 + 24 * q^58 - 2 * q^59 + 24 * q^61 + 54 * q^62 - 12 * q^63 + 281 * q^64 + 86 * q^66 - 20 * q^67 + 10 * q^68 - 18 * q^71 - 65 * q^72 + 22 * q^73 + 14 * q^74 - 28 * q^77 + 24 * q^79 + 315 * q^81 + 8 * q^82 - 20 * q^83 + 56 * q^84 - 40 * q^86 - 66 * q^87 - 16 * q^88 - 2 * q^89 + 24 * q^91 + 48 * q^92 - 40 * q^93 - 24 * q^94 - 26 * q^96 + 58 * q^97 + 23 * q^98 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9025))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	19
9025.2.a.a	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.i.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.b	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.i.a	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.c	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.b.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
9025.2.a.d	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				19.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.e	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.e.a	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+4q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.f	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓				361.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-3q^{7}-3q^{9}-5q^{11}+4q^{16}+\cdots\)
9025.2.a.g	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.e.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}+4q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.h	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.b.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
9025.2.a.i	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.i.a	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.j	$9025$	$2$	9025.a	1.a	$1$	$1$	$1$	$72.065$	\(\Q\)	None	✓				95.2.i.a	$1$	$1$	\(2\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.k	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				1805.2.a.c	$1$	$0$	\(-3\)	\(-3\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.l	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓	✓			9025.2.a.l	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.m	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓	✓			9025.2.a.l	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.n	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.c	$1$	$2$	\(-1\)	\(-3\)	\(0\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
9025.2.a.o	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.d	$1$	$0$	\(0\)	\(-4\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}-2q^{3}+3q^{4}+(-2+4\beta )q^{6}+\cdots\)
9025.2.a.p	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{19}) \)	\(\Q(\sqrt{-19}) \)	✓				1805.2.b.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-\beta q^{7}-3q^{9}+5q^{11}+4q^{16}+\cdots\)
9025.2.a.q	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				1805.2.a.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}+2q^{7}-\beta q^{8}-3q^{9}+\cdots\)
9025.2.a.r	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.d	$1$	$0$	\(0\)	\(4\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}+2q^{3}+3q^{4}+(2-4\beta )q^{6}+\cdots\)
9025.2.a.s	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.c	$1$	$0$	\(1\)	\(3\)	\(0\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.t	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓	✓			9025.2.a.l	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.u	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓	✓			9025.2.a.l	$1$	$0$	\(3\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.v	$9025$	$2$	9025.a	1.a	$1$	$2$	$2$	$72.065$	\(\Q(\sqrt{5}) \)	None	✓				1805.2.a.c	$1$	$0$	\(3\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(2+\cdots)q^{6}+\cdots\)
9025.2.a.w	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	\(\Q(\zeta_{14})^+\)	None	✓				475.2.a.d	$1$	$1$	\(-4\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.x	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	\(\Q(\zeta_{18})^+\)	None	✓				19.2.e.a	$1$	$0$	\(-3\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.y	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	3.3.169.1	None	✓				475.2.a.e	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
9025.2.a.z	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	3.3.361.1	None	✓				95.2.e.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
9025.2.a.ba	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	3.3.361.1	None	✓				95.2.e.b	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bb	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	3.3.148.1	None	✓				95.2.a.a	$1$	$0$	\(1\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
9025.2.a.bc	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	3.3.169.1	None	✓				475.2.a.e	$1$	$1$	\(2\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bd	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	\(\Q(\zeta_{18})^+\)	None	✓				19.2.e.a	$1$	$1$	\(3\)	\(3\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.be	$9025$	$2$	9025.a	1.a	$1$	$3$	$3$	$72.065$	\(\Q(\zeta_{14})^+\)	None	✓				475.2.a.d	$1$	$0$	\(4\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bf	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	4.4.11344.1	None	✓				95.2.a.b	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
9025.2.a.bg	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	4.4.7537.1	None	✓				95.2.e.c	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bh	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\sqrt{38 +2 \sqrt{5}})\)	None	✓				1805.2.a.j	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(11\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bi	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\zeta_{20})^+\)	None	✓				1805.2.a.k	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
9025.2.a.bj	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\zeta_{20})^+\)	None	✓				361.2.a.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-3+\cdots)q^{6}+\cdots\)
9025.2.a.bk	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\zeta_{20})^+\)	None	✓	✓			9025.2.a.bk	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bl	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\zeta_{20})^+\)	None	✓				1805.2.a.l	$2$	$1$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(3+\beta _{2}+\cdots)q^{6}+\cdots\)
9025.2.a.bm	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\zeta_{20})^+\)	None	✓	✓			9025.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bn	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\sqrt{3 + \sqrt{2}})\)	None	✓				1805.2.a.m	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
9025.2.a.bo	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	\(\Q(\sqrt{38 +2 \sqrt{5}})\)	None	✓				1805.2.a.j	$1$	$0$	\(1\)	\(1\)	\(0\)	\(11\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bp	$9025$	$2$	9025.a	1.a	$1$	$4$	$4$	$72.065$	4.4.7537.1	None	✓				95.2.e.c	$1$	$0$	\(1\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bq	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.5822000.1	None	✓				1805.2.a.q	$1$	$0$	\(-2\)	\(-4\)	\(0\)	\(-7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9025.2.a.br	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.41289040.1	None	✓				475.2.e.f	$1$	$1$	\(-2\)	\(-3\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.bs	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.41289040.1	None	✓				475.2.e.f	$1$	$1$	\(-2\)	\(-3\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(-\beta _{3}+\beta _{4})q^{4}+\cdots\)
9025.2.a.bt	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.4227136.1	None	✓				95.2.i.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
9025.2.a.bu	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.4227136.1	None	✓				95.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
9025.2.a.bv	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.71593280.1	None	✓	✓			9025.2.a.bv	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bw	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.71593280.1	None	✓	✓			9025.2.a.bv	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bx	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.66064384.1	None	✓				95.2.b.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.by	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.41289040.1	None	✓				475.2.e.f	$1$	$0$	\(2\)	\(3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.bz	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.41289040.1	None	✓				475.2.e.f	$1$	$0$	\(2\)	\(3\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.ca	$9025$	$2$	9025.a	1.a	$1$	$6$	$6$	$72.065$	6.6.5822000.1	None	✓				1805.2.a.q	$1$	$0$	\(2\)	\(4\)	\(0\)	\(-7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4})q^{3}+\cdots\)
9025.2.a.cb	$9025$	$2$	9025.a	1.a	$1$	$8$	$8$	$72.065$	8.8.\(\cdots\).1	\(\Q(\sqrt{-95}) \)	✓				1805.2.b.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{4}$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
9025.2.a.cc	$9025$	$2$	9025.a	1.a	$1$	$9$	$9$	$72.065$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.2.k.a	$1$	$1$	\(-6\)	\(-9\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
9025.2.a.cd	$9025$	$2$	9025.a	1.a	$1$	$9$	$9$	$72.065$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.2.k.b	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.ce	$9025$	$2$	9025.a	1.a	$1$	$9$	$9$	$72.065$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.2.k.b	$1$	$1$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9025.2.a.cf	$9025$	$2$	9025.a	1.a	$1$	$9$	$9$	$72.065$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.2.k.a	$1$	$0$	\(6\)	\(9\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
9025.2.a.cg	$9025$	$2$	9025.a	1.a	$1$	$10$	$10$	$72.065$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			9025.2.a.cg	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{7}-\beta _{8})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.ch	$9025$	$2$	9025.a	1.a	$1$	$10$	$10$	$72.065$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			9025.2.a.cg	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{7}-\beta _{8})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.ci	$9025$	$2$	9025.a	1.a	$1$	$10$	$10$	$72.065$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			9025.2.a.cg	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{4}-\beta _{7}+\beta _{8})q^{3}+\cdots\)
9025.2.a.cj	$9025$	$2$	9025.a	1.a	$1$	$10$	$10$	$72.065$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			9025.2.a.cg	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{4}-\beta _{7}+\beta _{8})q^{3}+\cdots\)
9025.2.a.ck	$9025$	$2$	9025.a	1.a	$1$	$16$	$16$	$72.065$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1805.2.b.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cl	$9025$	$2$	9025.a	1.a	$1$	$16$	$16$	$72.065$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1805.2.b.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cm	$9025$	$2$	9025.a	1.a	$1$	$16$	$16$	$72.065$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1805.2.a.w	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-22\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)
9025.2.a.cn	$9025$	$2$	9025.a	1.a	$1$	$20$	$20$	$72.065$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			9025.2.a.cn	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.co	$9025$	$2$	9025.a	1.a	$1$	$20$	$20$	$72.065$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			9025.2.a.cn	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cp	$9025$	$2$	9025.a	1.a	$1$	$21$	$21$	$72.065$		None	✓				475.2.l.d	$1$	$1$	\(-6\)	\(-9\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
9025.2.a.cq	$9025$	$2$	9025.a	1.a	$1$	$21$	$21$	$72.065$		None	✓		✓		475.2.l.d	$1$	$1$	\(-6\)	\(-9\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
9025.2.a.cr	$9025$	$2$	9025.a	1.a	$1$	$21$	$21$	$72.065$		None	✓		✓		475.2.l.d	$1$	$0$	\(6\)	\(9\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
9025.2.a.cs	$9025$	$2$	9025.a	1.a	$1$	$21$	$21$	$72.065$		None	✓				475.2.l.d	$1$	$0$	\(6\)	\(9\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
9025.2.a.ct	$9025$	$2$	9025.a	1.a	$1$	$24$	$24$	$72.065$		None	✓		✓		95.2.p.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
9025.2.a.cu	$9025$	$2$	9025.a	1.a	$1$	$24$	$24$	$72.065$		None	✓				95.2.p.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
9025.2.a.cv	$9025$	$2$	9025.a	1.a	$1$	$40$	$40$	$72.065$		None	✓		✓		1805.2.b.m	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9025)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 2}\)