Space of modular forms of level 4275, weight 2, and trivial character

• Label: 4275.2.a
• Level: $4275$
• Weight: $2$
• Character orbit: 4275.a
• Rep. character: $\chi_{4275}(1,\cdot)$
• Character field: $\Q$
• Dimension: $142$
• Newform subspaces: $50$
• Sturm bound: $1200$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4275.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(1200\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4275))\).

	Total	New	Old
Modular forms	624	142	482
Cusp forms	577	142	435
Eisenstein series	47	0	47

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

\(3\)	\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(72\)	\(12\)	\(60\)		\(67\)	\(12\)	\(55\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(84\)	\(16\)	\(68\)		\(78\)	\(16\)	\(62\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(80\)	\(18\)	\(62\)		\(74\)	\(18\)	\(56\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(76\)	\(10\)	\(66\)		\(70\)	\(10\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(84\)	\(21\)	\(63\)		\(78\)	\(21\)	\(57\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(72\)	\(19\)	\(53\)		\(66\)	\(19\)	\(47\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(76\)	\(21\)	\(55\)		\(70\)	\(21\)	\(49\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(80\)	\(25\)	\(55\)		\(74\)	\(25\)	\(49\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(296\)	\(62\)	\(234\)		\(273\)	\(62\)	\(211\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(328\)	\(80\)	\(248\)		\(304\)	\(80\)	\(224\)		\(24\)	\(0\)	\(24\)

Trace form

142 * q + q^2 + 143 * q^4 + 5 * q^7 - 3 * q^8 + 13 * q^11 - 2 * q^13 - 12 * q^14 + 145 * q^16 - 11 * q^17 - 2 * q^19 + 4 * q^22 - 8 * q^23 + 6 * q^26 + 18 * q^28 + 32 * q^29 + 5 * q^32 + 18 * q^34 - 12 * q^37 - 3 * q^38 + 13 * q^43 + 66 * q^44 + 36 * q^46 - q^47 + 145 * q^49 + 14 * q^52 + 26 * q^53 + 8 * q^56 + 10 * q^58 - 18 * q^59 - 9 * q^61 + 8 * q^62 + 185 * q^64 + 12 * q^67 - 52 * q^68 - 42 * q^71 + q^73 + 62 * q^74 - 5 * q^76 - 41 * q^77 + 8 * q^79 + 38 * q^82 + 16 * q^83 + 4 * q^86 - 32 * q^88 - 2 * q^89 - 16 * q^91 + 40 * q^92 - 32 * q^94 - 6 * q^97 + 5 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	19
4275.2.a.a	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				57.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{7}+3q^{11}+6q^{13}+\cdots\)
4275.2.a.b	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				57.2.a.a	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+5q^{7}-q^{11}-2q^{13}+\cdots\)
4275.2.a.c	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				1425.2.a.e	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{7}+3q^{8}-3q^{11}+\cdots\)
4275.2.a.d	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				855.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}-2q^{11}+\cdots\)
4275.2.a.e	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				95.2.b.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots\)
4275.2.a.f	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				1425.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}-5q^{11}-4q^{13}+\cdots\)
4275.2.a.g	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				855.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{7}+3q^{8}+2q^{11}+\cdots\)
4275.2.a.h	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				285.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{7}+3q^{8}+6q^{11}+\cdots\)
4275.2.a.i	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				19.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
4275.2.a.j	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				285.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots\)
4275.2.a.k	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				855.2.c.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{7}-3q^{8}+2q^{11}+\cdots\)
4275.2.a.l	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				1425.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-5q^{11}+4q^{13}+\cdots\)
4275.2.a.m	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				57.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-6q^{13}-q^{16}+\cdots\)
4275.2.a.n	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				855.2.c.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{7}-3q^{8}-2q^{11}+\cdots\)
4275.2.a.o	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				285.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{7}-3q^{8}+2q^{11}+\cdots\)
4275.2.a.p	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				95.2.b.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{7}-3q^{8}+4q^{11}+\cdots\)
4275.2.a.q	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	\(\Q\)	None	✓				1425.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{11}+\cdots\)
4275.2.a.r	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{5}) \)	None	✓				1425.2.a.m	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-2\beta )q^{7}+\cdots\)
4275.2.a.s	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{5}) \)	None	✓				1425.2.a.n	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
4275.2.a.t	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{3}) \)	None	✓				285.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+(1-\beta )q^{7}-\beta q^{8}+(-3+\cdots)q^{11}+\cdots\)
4275.2.a.u	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{7}) \)	None	✓				285.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}+(1+\beta )q^{7}+3\beta q^{8}+\cdots\)
4275.2.a.v	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{5}) \)	None	✓				1425.2.a.n	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
4275.2.a.w	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{5}) \)	None	✓				1425.2.a.m	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots\)
4275.2.a.x	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{2}) \)	None	✓				285.2.a.f	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2-\beta )q^{7}+\cdots\)
4275.2.a.y	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	\(\Q(\sqrt{2}) \)	None	✓				285.2.a.g	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+\beta q^{7}+(3+\cdots)q^{8}+\cdots\)
4275.2.a.z	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	\(\Q(\zeta_{14})^+\)	None	✓				475.2.a.d	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
4275.2.a.ba	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.169.1	None	✓				475.2.a.e	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4275.2.a.bb	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.h	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(-1+\cdots)q^{8}+\cdots\)
4275.2.a.bc	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.j	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bd	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				285.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(3-\beta _{1})q^{7}+\cdots\)
4275.2.a.be	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.621.1	None	✓				1425.2.a.u	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{7}+\cdots\)
4275.2.a.bf	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.837.1	None	✓				1425.2.a.t	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4275.2.a.bg	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.837.1	None	✓				1425.2.a.t	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bh	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.621.1	None	✓				1425.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+\cdots\)
4275.2.a.bi	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				285.2.c.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bj	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.h	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots\)
4275.2.a.bk	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				95.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-2\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots\)
4275.2.a.bl	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.j	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bm	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.169.1	None	✓				475.2.a.e	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
4275.2.a.bn	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	\(\Q(\zeta_{14})^+\)	None	✓				475.2.a.d	$1$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bo	$4275$	$2$	4275.a	1.a	$1$	$4$	$4$	$34.136$	4.4.11344.1	None	✓		✓		95.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bp	$4275$	$2$	4275.a	1.a	$1$	$4$	$4$	$34.136$	4.4.13068.1	None	✓				171.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-1+\beta _{3})q^{7}+\cdots\)
4275.2.a.bq	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.15044092.1	None	✓	✓	✓		4275.2.a.bq	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(-1+\beta _{1}-\beta _{5})q^{7}+\cdots\)
4275.2.a.br	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.66064384.1	None	✓		✓		95.2.b.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
4275.2.a.bs	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.16717036.1	None	✓	✓	✓		4275.2.a.bs	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
4275.2.a.bt	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.16717036.1	None	✓	✓			4275.2.a.bs	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{2}-\beta _{4})q^{7}+\cdots\)
4275.2.a.bu	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.15044092.1	None	✓	✓	✓		4275.2.a.bq	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(1-\beta _{1}+\beta _{5})q^{7}+\cdots\)
4275.2.a.bv	$4275$	$2$	4275.a	1.a	$1$	$7$	$7$	$34.136$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				285.2.c.b	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{7}+\cdots\)
4275.2.a.bw	$4275$	$2$	4275.a	1.a	$1$	$7$	$7$	$34.136$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				285.2.c.b	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
4275.2.a.bx	$4275$	$2$	4275.a	1.a	$1$	$12$	$12$	$34.136$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		855.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{11}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(1+\beta _{6})q^{4}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4275)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\)\(^{\oplus 2}\)