Space of modular forms of level 7865, weight 2, and trivial character

• Label: 7865.2.a
• Level: $7865$
• Weight: $2$
• Character orbit: 7865.a
• Rep. character: $\chi_{7865}(1,\cdot)$
• Character field: $\Q$
• Dimension: $436$
• Newform subspaces: $42$
• Sturm bound: $1848$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7865.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(1848\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7865))\).

	Total	New	Old
Modular forms	948	436	512
Cusp forms	901	436	465
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.

\(5\)	\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(111\)	\(55\)	\(56\)		\(106\)	\(55\)	\(51\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(123\)	\(59\)	\(64\)		\(117\)	\(59\)	\(58\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(124\)	\(55\)	\(69\)		\(118\)	\(55\)	\(63\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(116\)	\(50\)	\(66\)		\(110\)	\(50\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(123\)	\(57\)	\(66\)		\(117\)	\(57\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(111\)	\(45\)	\(66\)		\(105\)	\(45\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(116\)	\(50\)	\(66\)		\(110\)	\(50\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(124\)	\(65\)	\(59\)		\(118\)	\(65\)	\(53\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(454\)	\(200\)	\(254\)		\(431\)	\(200\)	\(231\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(494\)	\(236\)	\(258\)		\(470\)	\(236\)	\(234\)		\(24\)	\(0\)	\(24\)

Trace form

436 * q + 6 * q^2 + 4 * q^3 + 436 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 18 * q^8 + 444 * q^9 - 4 * q^10 - 8 * q^12 + 2 * q^13 - 16 * q^14 - 4 * q^15 + 452 * q^16 + 12 * q^17 + 10 * q^18 - 6 * q^20 - 4 * q^21 + 16 * q^23 - 32 * q^24 + 436 * q^25 + 28 * q^27 + 28 * q^28 - 4 * q^30 - 4 * q^31 + 22 * q^32 + 8 * q^34 - 4 * q^35 + 476 * q^36 + 32 * q^37 + 20 * q^38 - 24 * q^40 + 20 * q^41 + 60 * q^42 + 24 * q^43 - 18 * q^45 - 16 * q^46 - 20 * q^47 + 52 * q^48 + 452 * q^49 + 6 * q^50 - 32 * q^51 + 6 * q^52 + 8 * q^53 + 36 * q^54 - 8 * q^56 + 52 * q^57 + 24 * q^58 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 4 * q^63 + 468 * q^64 + 4 * q^65 + 36 * q^67 - 36 * q^68 + 8 * q^69 + 8 * q^70 - 40 * q^71 + 94 * q^72 + 48 * q^73 + 32 * q^74 + 4 * q^75 - 20 * q^76 + 16 * q^78 + 24 * q^79 - 14 * q^80 + 436 * q^81 + 88 * q^82 - 44 * q^83 + 132 * q^84 - 16 * q^85 + 44 * q^87 + 24 * q^89 - 8 * q^90 + 4 * q^91 + 92 * q^92 - 12 * q^93 + 32 * q^94 - 8 * q^95 - 108 * q^96 + 28 * q^97 - 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7865))\) 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	11	13
7865.2.a.a	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	\(\Q\)	None	✓	✓			7865.2.a.a	$1$	$1$	\(-1\)	\(3\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}-q^{5}-3q^{6}-2q^{7}+\cdots\)
7865.2.a.b	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	\(\Q\)	None	✓				715.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+q^{5}-2q^{7}+q^{9}+4q^{12}+\cdots\)
7865.2.a.c	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	\(\Q\)	None	✓				65.2.a.a	$1$	$1$	\(1\)	\(-2\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
7865.2.a.d	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	\(\Q\)	None	✓	✓			7865.2.a.a	$1$	$0$	\(1\)	\(3\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-q^{4}-q^{5}+3q^{6}+2q^{7}+\cdots\)
7865.2.a.e	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	\(\Q\)	None	✓				715.2.a.a	$1$	$1$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-3q^{9}+2q^{10}+\cdots\)
7865.2.a.f	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	\(\Q(\sqrt{5}) \)	None	✓				715.2.v.a	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
7865.2.a.g	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	\(\Q(\sqrt{2}) \)	None	✓				715.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+\beta q^{3}+q^{5}+2q^{6}+(2+\beta )q^{7}+\cdots\)
7865.2.a.h	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	\(\Q(\sqrt{3}) \)	None	✓				65.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(3+\beta )q^{6}+\cdots\)
7865.2.a.i	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	\(\Q(\sqrt{5}) \)	None	✓				715.2.v.a	$1$	$1$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
7865.2.a.j	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	\(\Q(\sqrt{2}) \)	None	✓				65.2.a.b	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
7865.2.a.k	$7865$	$2$	7865.a	1.a	$1$	$3$	$3$	$62.802$	3.3.148.1	None	✓				715.2.a.e	$1$	$0$	\(-2\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7865.2.a.l	$7865$	$2$	7865.a	1.a	$1$	$3$	$3$	$62.802$	3.3.148.1	None	✓				715.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
7865.2.a.m	$7865$	$2$	7865.a	1.a	$1$	$4$	$4$	$62.802$	4.4.6224.1	None	✓	✓			7865.2.a.m	$1$	$1$	\(-2\)	\(2\)	\(4\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
7865.2.a.n	$7865$	$2$	7865.a	1.a	$1$	$4$	$4$	$62.802$	4.4.6224.1	None	✓	✓			7865.2.a.m	$1$	$0$	\(2\)	\(2\)	\(4\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
7865.2.a.o	$7865$	$2$	7865.a	1.a	$1$	$6$	$6$	$62.802$	6.6.37261816.1	None	✓				715.2.a.g	$1$	$1$	\(1\)	\(-4\)	\(-6\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
7865.2.a.p	$7865$	$2$	7865.a	1.a	$1$	$6$	$6$	$62.802$	6.6.3486377.1	None	✓				715.2.a.f	$1$	$0$	\(5\)	\(-2\)	\(-6\)	\(8\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{4})q^{2}-\beta _{5}q^{3}+(1+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
7865.2.a.q	$7865$	$2$	7865.a	1.a	$1$	$7$	$7$	$62.802$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			7865.2.a.q	$1$	$1$	\(0\)	\(0\)	\(7\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.r	$7865$	$2$	7865.a	1.a	$1$	$7$	$7$	$62.802$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			7865.2.a.q	$1$	$0$	\(0\)	\(0\)	\(7\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.s	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				715.2.a.h	$1$	$1$	\(-2\)	\(0\)	\(8\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.t	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			7865.2.a.t	$1$	$1$	\(-1\)	\(-5\)	\(-8\)	\(-9\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
7865.2.a.u	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			7865.2.a.t	$1$	$0$	\(1\)	\(-5\)	\(-8\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
7865.2.a.v	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			7865.2.a.v	$1$	$1$	\(-1\)	\(-2\)	\(9\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.w	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				715.2.a.i	$1$	$0$	\(-1\)	\(2\)	\(9\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.x	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			7865.2.a.x	$1$	$0$	\(0\)	\(-2\)	\(-9\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7865.2.a.y	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			7865.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(-9\)	\(-9\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7865.2.a.z	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			7865.2.a.v	$1$	$0$	\(1\)	\(-2\)	\(9\)	\(10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.ba	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			7865.2.a.ba	$1$	$1$	\(-1\)	\(2\)	\(-11\)	\(-10\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7865.2.a.bb	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			7865.2.a.bb	$1$	$1$	\(0\)	\(2\)	\(11\)	\(-9\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.bc	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			7865.2.a.bb	$1$	$0$	\(0\)	\(2\)	\(11\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.bd	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			7865.2.a.ba	$1$	$0$	\(1\)	\(2\)	\(-11\)	\(10\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7865.2.a.be	$7865$	$2$	7865.a	1.a	$1$	$16$	$16$	$62.802$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				715.2.v.b	$1$	$1$	\(-2\)	\(-7\)	\(16\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{8}-\beta _{9})q^{4}+\cdots\)
7865.2.a.bf	$7865$	$2$	7865.a	1.a	$1$	$16$	$16$	$62.802$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		715.2.v.b	$1$	$1$	\(2\)	\(-7\)	\(16\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{8}-\beta _{9})q^{4}+\cdots\)
7865.2.a.bg	$7865$	$2$	7865.a	1.a	$1$	$18$	$18$	$62.802$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		7865.2.a.bg	$1$	$1$	\(-2\)	\(-4\)	\(18\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.bh	$7865$	$2$	7865.a	1.a	$1$	$18$	$18$	$62.802$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			7865.2.a.bg	$1$	$0$	\(2\)	\(-4\)	\(18\)	\(20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7865.2.a.bi	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓	✓			7865.2.a.bi	$1$	$1$	\(-2\)	\(4\)	\(-22\)	\(-20\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
7865.2.a.bj	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓				715.2.v.c	$1$	$1$	\(-1\)	\(-7\)	\(-22\)	\(-5\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
7865.2.a.bk	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓		✓		715.2.v.c	$1$	$1$	\(1\)	\(-7\)	\(-22\)	\(5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
7865.2.a.bl	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓	✓			7865.2.a.bi	$1$	$0$	\(2\)	\(4\)	\(-22\)	\(20\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7865.2.a.bm	$7865$	$2$	7865.a	1.a	$1$	$26$	$26$	$62.802$		None	✓		✓		715.2.v.d	$1$	$0$	\(-1\)	\(9\)	\(-26\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7865.2.a.bn	$7865$	$2$	7865.a	1.a	$1$	$26$	$26$	$62.802$		None	✓		✓		715.2.v.d	$1$	$0$	\(1\)	\(9\)	\(-26\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
7865.2.a.bo	$7865$	$2$	7865.a	1.a	$1$	$30$	$30$	$62.802$		None	✓		✓		715.2.v.e	$1$	$0$	\(-1\)	\(9\)	\(30\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
7865.2.a.bp	$7865$	$2$	7865.a	1.a	$1$	$30$	$30$	$62.802$		None	✓		✓		715.2.v.e	$1$	$0$	\(1\)	\(9\)	\(30\)	\(5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7865))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7865)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(715))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\)\(^{\oplus 2}\)