Space of modular forms of level 7935, weight 2, and trivial character

• Label: 7935.2.a
• Level: $7935$
• Weight: $2$
• Character orbit: 7935.a
• Rep. character: $\chi_{7935}(1,\cdot)$
• Character field: $\Q$
• Dimension: $336$
• Newform subspaces: $49$
• Sturm bound: $2208$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(2208\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7935))\).

	Total	New	Old
Modular forms	1152	336	816
Cusp forms	1057	336	721
Eisenstein series	95	0	95

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

\(3\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(132\)	\(41\)	\(91\)		\(121\)	\(41\)	\(80\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(154\)	\(44\)	\(110\)		\(142\)	\(44\)	\(98\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(156\)	\(51\)	\(105\)		\(144\)	\(51\)	\(93\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(134\)	\(33\)	\(101\)		\(122\)	\(33\)	\(89\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(144\)	\(43\)	\(101\)		\(132\)	\(43\)	\(89\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(144\)	\(40\)	\(104\)		\(132\)	\(40\)	\(92\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(144\)	\(33\)	\(111\)		\(132\)	\(33\)	\(99\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(144\)	\(51\)	\(93\)		\(132\)	\(51\)	\(81\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(554\)	\(147\)	\(407\)		\(507\)	\(147\)	\(360\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(598\)	\(189\)	\(409\)		\(550\)	\(189\)	\(361\)		\(48\)	\(0\)	\(48\)

Trace form

336 * q + 4 * q^2 - 2 * q^3 + 340 * q^4 + 2 * q^6 + 12 * q^8 + 336 * q^9 + 4 * q^10 + 16 * q^11 - 6 * q^12 - 8 * q^13 - 8 * q^14 + 2 * q^15 + 340 * q^16 + 4 * q^18 + 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^22 - 6 * q^24 + 336 * q^25 + 24 * q^26 - 2 * q^27 + 8 * q^28 + 16 * q^29 + 2 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^34 + 8 * q^35 + 340 * q^36 + 16 * q^37 + 8 * q^38 - 4 * q^39 + 12 * q^40 + 24 * q^41 + 8 * q^43 + 24 * q^44 + 16 * q^47 + 2 * q^48 + 328 * q^49 + 4 * q^50 + 12 * q^51 - 32 * q^52 - 8 * q^53 + 2 * q^54 - 32 * q^56 - 16 * q^57 + 24 * q^58 + 6 * q^60 - 16 * q^61 - 32 * q^62 + 348 * q^64 + 16 * q^65 + 16 * q^66 + 8 * q^67 + 24 * q^68 - 24 * q^70 + 24 * q^71 + 12 * q^72 + 8 * q^73 - 2 * q^75 - 40 * q^77 - 28 * q^78 + 8 * q^79 + 336 * q^81 + 32 * q^82 - 8 * q^83 - 8 * q^84 + 8 * q^85 - 20 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 32 * q^91 - 16 * q^93 + 24 * q^94 - 30 * q^96 + 44 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\) 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	23
7935.2.a.a	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{7}+\cdots\)
7935.2.a.b	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+5q^{7}+\cdots\)
7935.2.a.c	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.a	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
7935.2.a.d	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				15.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
7935.2.a.e	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.b	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
7935.2.a.f	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
7935.2.a.g	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
7935.2.a.h	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
7935.2.a.i	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.d	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+3q^{7}+q^{9}+4q^{11}+\cdots\)
7935.2.a.j	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.e	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
7935.2.a.k	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓				345.2.a.f	$1$	$0$	\(2\)	\(-1\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-3q^{7}+\cdots\)
7935.2.a.l	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.l	$1$	$1$	\(2\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
7935.2.a.m	$7935$	$2$	7935.a	1.a	$1$	$1$	$1$	$63.361$	\(\Q\)	None	✓	✓			7935.2.a.l	$1$	$0$	\(2\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
7935.2.a.n	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{3}) \)	None	✓				345.2.a.g	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots\)
7935.2.a.o	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{2}) \)	None	✓	✓			7935.2.a.o	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}+(2-2\beta )q^{7}+\cdots\)
7935.2.a.p	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{2}) \)	None	✓	✓			7935.2.a.o	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}+(-2+2\beta )q^{7}+\cdots\)
7935.2.a.q	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{2}) \)	None	✓				345.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}+(1+2\beta )q^{7}+\cdots\)
7935.2.a.r	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{73}) \)	None	✓	✓			7935.2.a.r	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}-\beta q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7935.2.a.s	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{73}) \)	None	✓	✓			7935.2.a.r	$1$	$0$	\(0\)	\(2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+\beta q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7935.2.a.t	$7935$	$2$	7935.a	1.a	$1$	$2$	$2$	$63.361$	\(\Q(\sqrt{6}) \)	None	✓				345.2.a.i	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
7935.2.a.u	$7935$	$2$	7935.a	1.a	$1$	$3$	$3$	$63.361$	3.3.316.1	None	✓				345.2.a.j	$1$	$1$	\(-1\)	\(3\)	\(-3\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.v	$7935$	$2$	7935.a	1.a	$1$	$3$	$3$	$63.361$	3.3.148.1	None	✓	✓			7935.2.a.v	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
7935.2.a.w	$7935$	$2$	7935.a	1.a	$1$	$3$	$3$	$63.361$	3.3.148.1	None	✓	✓			7935.2.a.v	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots\)
7935.2.a.x	$7935$	$2$	7935.a	1.a	$1$	$3$	$3$	$63.361$	3.3.756.1	None	✓	✓			7935.2.a.x	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.y	$7935$	$2$	7935.a	1.a	$1$	$3$	$3$	$63.361$	3.3.756.1	None	✓	✓			7935.2.a.x	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.z	$7935$	$2$	7935.a	1.a	$1$	$4$	$4$	$63.361$	4.4.25492.1	None	✓	✓			7935.2.a.z	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2}+\beta _{3})q^{4}-q^{5}+\cdots\)
7935.2.a.ba	$7935$	$2$	7935.a	1.a	$1$	$4$	$4$	$63.361$	4.4.25492.1	None	✓	✓			7935.2.a.z	$1$	$0$	\(0\)	\(4\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots\)
7935.2.a.bb	$7935$	$2$	7935.a	1.a	$1$	$5$	$5$	$63.361$	5.5.3370660.1	None	✓	✓			7935.2.a.bb	$1$	$1$	\(0\)	\(5\)	\(-5\)	\(-3\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bc	$7935$	$2$	7935.a	1.a	$1$	$5$	$5$	$63.361$	5.5.3370660.1	None	✓	✓			7935.2.a.bb	$1$	$0$	\(0\)	\(5\)	\(5\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bd	$7935$	$2$	7935.a	1.a	$1$	$6$	$6$	$63.361$	6.6.22733568.1	None	✓	✓			7935.2.a.bd	$1$	$0$	\(0\)	\(-6\)	\(-6\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.be	$7935$	$2$	7935.a	1.a	$1$	$6$	$6$	$63.361$	6.6.22733568.1	None	✓	✓			7935.2.a.bd	$1$	$1$	\(0\)	\(-6\)	\(6\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bf	$7935$	$2$	7935.a	1.a	$1$	$6$	$6$	$63.361$	6.6.4507648.1	None	✓	✓			7935.2.a.bf	$1$	$0$	\(0\)	\(6\)	\(-6\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
7935.2.a.bg	$7935$	$2$	7935.a	1.a	$1$	$6$	$6$	$63.361$	6.6.4507648.1	None	✓	✓			7935.2.a.bf	$1$	$1$	\(0\)	\(6\)	\(6\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
7935.2.a.bh	$7935$	$2$	7935.a	1.a	$1$	$8$	$8$	$63.361$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			7935.2.a.bh	$1$	$1$	\(0\)	\(8\)	\(-8\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bi	$7935$	$2$	7935.a	1.a	$1$	$8$	$8$	$63.361$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			7935.2.a.bh	$1$	$0$	\(0\)	\(8\)	\(8\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bj	$7935$	$2$	7935.a	1.a	$1$	$10$	$10$	$63.361$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			7935.2.a.bj	$1$	$1$	\(0\)	\(-10\)	\(-10\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bk	$7935$	$2$	7935.a	1.a	$1$	$10$	$10$	$63.361$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			7935.2.a.bj	$1$	$0$	\(0\)	\(-10\)	\(10\)	\(6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bl	$7935$	$2$	7935.a	1.a	$1$	$12$	$12$	$63.361$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7935.2.a.bl	$1$	$0$	\(0\)	\(12\)	\(-12\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{7}-\beta _{8})q^{4}-q^{5}+\cdots\)
7935.2.a.bm	$7935$	$2$	7935.a	1.a	$1$	$12$	$12$	$63.361$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7935.2.a.bl	$1$	$1$	\(0\)	\(12\)	\(12\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{7}-\beta _{8})q^{4}+q^{5}+\cdots\)
7935.2.a.bn	$7935$	$2$	7935.a	1.a	$1$	$15$	$15$	$63.361$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		345.2.m.b	$1$	$1$	\(-8\)	\(15\)	\(-15\)	\(13\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7935.2.a.bo	$7935$	$2$	7935.a	1.a	$1$	$15$	$15$	$63.361$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		345.2.m.b	$1$	$1$	\(-8\)	\(15\)	\(15\)	\(-13\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7935.2.a.bp	$7935$	$2$	7935.a	1.a	$1$	$15$	$15$	$63.361$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				345.2.m.a	$1$	$1$	\(0\)	\(-15\)	\(-15\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
7935.2.a.bq	$7935$	$2$	7935.a	1.a	$1$	$15$	$15$	$63.361$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		345.2.m.a	$1$	$1$	\(0\)	\(-15\)	\(15\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
7935.2.a.br	$7935$	$2$	7935.a	1.a	$1$	$16$	$16$	$63.361$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		7935.2.a.br	$1$	$1$	\(0\)	\(-16\)	\(-16\)	\(-12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bs	$7935$	$2$	7935.a	1.a	$1$	$16$	$16$	$63.361$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			7935.2.a.br	$1$	$0$	\(0\)	\(-16\)	\(16\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bt	$7935$	$2$	7935.a	1.a	$1$	$25$	$25$	$63.361$		None	✓		✓		345.2.m.d	$1$	$0$	\(1\)	\(-25\)	\(-25\)	\(15\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7935.2.a.bu	$7935$	$2$	7935.a	1.a	$1$	$25$	$25$	$63.361$		None	✓		✓		345.2.m.d	$1$	$0$	\(1\)	\(-25\)	\(25\)	\(-15\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
7935.2.a.bv	$7935$	$2$	7935.a	1.a	$1$	$25$	$25$	$63.361$		None	✓		✓		345.2.m.c	$1$	$0$	\(11\)	\(25\)	\(-25\)	\(-7\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
7935.2.a.bw	$7935$	$2$	7935.a	1.a	$1$	$25$	$25$	$63.361$		None	✓		✓		345.2.m.c	$1$	$0$	\(11\)	\(25\)	\(25\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7935))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7935)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\)\(^{\oplus 2}\)