Space of modular forms of level 5082, weight 2, and trivial character

• Label: 5082.2.a
• Level: $5082$
• Weight: $2$
• Character orbit: 5082.a
• Rep. character: $\chi_{5082}(1,\cdot)$
• Character field: $\Q$
• Dimension: $110$
• Newform subspaces: $59$
• Sturm bound: $2112$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5082.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 59 \)
Sturm bound:			\(2112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5082))\).

	Total	New	Old
Modular forms	1104	110	994
Cusp forms	1009	110	899
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.

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(4\)
Plus space				\(+\)	\(44\)
Minus space				\(-\)	\(66\)

Trace form

110 * q + 2 * q^2 + 110 * q^4 + 4 * q^5 + 2 * q^8 + 110 * q^9 + 4 * q^10 - 12 * q^13 - 8 * q^15 + 110 * q^16 + 4 * q^17 + 2 * q^18 + 4 * q^20 - 2 * q^21 + 114 * q^25 + 4 * q^26 + 28 * q^29 - 8 * q^30 - 32 * q^31 + 2 * q^32 + 4 * q^34 + 8 * q^35 + 110 * q^36 + 4 * q^37 - 8 * q^39 + 4 * q^40 + 20 * q^41 + 2 * q^42 + 4 * q^45 - 8 * q^46 - 16 * q^47 + 110 * q^49 - 2 * q^50 - 8 * q^51 - 12 * q^52 - 4 * q^53 - 24 * q^57 - 4 * q^58 - 8 * q^60 + 4 * q^61 + 110 * q^64 - 8 * q^65 - 24 * q^67 + 4 * q^68 + 2 * q^72 + 4 * q^73 + 28 * q^74 + 8 * q^78 + 48 * q^79 + 4 * q^80 + 110 * q^81 - 12 * q^82 + 16 * q^83 - 2 * q^84 - 8 * q^85 - 8 * q^86 + 36 * q^89 + 4 * q^90 + 8 * q^91 + 8 * q^93 + 16 * q^95 + 20 * q^97 + 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	11
5082.2.a.a	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.e	$1$	$0$	\(-1\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.b	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.b	$1$	$0$	\(-1\)	\(-1\)	\(-4\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.c	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.c	$1$	$2$	\(-1\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.d	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				42.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.e	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.f	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.f	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.g	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.g	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.h	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.h	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.i	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.i	$1$	$0$	\(-1\)	\(-1\)	\(4\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.j	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.j	$1$	$1$	\(-1\)	\(1\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.k	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.k	$1$	$1$	\(-1\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.l	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.f	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.m	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.m	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.n	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.g	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.o	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.p	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.q	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.a	$1$	$1$	\(1\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.r	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.e	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.s	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.t	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.f	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.u	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.h	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.v	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.w	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.x	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.i	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.y	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.j	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.z	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.k	$1$	$1$	\(1\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.ba	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓				462.2.a.d	$1$	$1$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.bb	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	\(\Q\)	None	✓	✓			5082.2.a.m	$1$	$0$	\(1\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bc	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bc	$1$	$0$	\(-2\)	\(-2\)	\(-4\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bd	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓		✓		462.2.j.b	$1$	$0$	\(-2\)	\(-2\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.be	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.be	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bf	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓				462.2.j.d	$1$	$0$	\(-2\)	\(-2\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bg	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bg	$1$	$0$	\(-2\)	\(-2\)	\(4\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bh	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓				462.2.j.c	$1$	$0$	\(-2\)	\(2\)	\(-5\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bi	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bi	$1$	$1$	\(-2\)	\(2\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bj	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓				462.2.j.a	$1$	$0$	\(-2\)	\(2\)	\(-1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bk	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓	✓			5082.2.a.bk	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bl	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{33}) \)	None	✓	✓			5082.2.a.bl	$1$	$0$	\(-2\)	\(2\)	\(3\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bm	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bc	$1$	$0$	\(2\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bn	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓				462.2.j.b	$1$	$1$	\(2\)	\(-2\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bo	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.be	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bp	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓		✓		462.2.j.d	$1$	$1$	\(2\)	\(-2\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bq	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bg	$1$	$0$	\(2\)	\(-2\)	\(4\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.br	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓		✓		462.2.j.c	$1$	$1$	\(2\)	\(2\)	\(-5\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bs	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓	✓			5082.2.a.bi	$1$	$1$	\(2\)	\(2\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bt	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓				462.2.j.a	$1$	$1$	\(2\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bu	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{3}) \)	None	✓				462.2.a.h	$1$	$0$	\(2\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bv	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{5}) \)	None	✓	✓			5082.2.a.bk	$1$	$0$	\(2\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bw	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	\(\Q(\sqrt{33}) \)	None	✓	✓			5082.2.a.bl	$1$	$0$	\(2\)	\(2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bx	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.8000.1	None	✓		✓		462.2.j.f	$1$	$1$	\(-4\)	\(-4\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.by	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.28400.1	None	✓		✓		462.2.j.h	$1$	$1$	\(-4\)	\(-4\)	\(4\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots\)
5082.2.a.bz	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	\(\Q(\sqrt{3}, \sqrt{5})\)	None	✓		✓		462.2.j.g	$1$	$1$	\(-4\)	\(4\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{6}+\cdots\)
5082.2.a.ca	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.4400.1	None	✓		✓		462.2.j.e	$1$	$1$	\(-4\)	\(4\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cb	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.69264.1	None	✓	✓	✓		5082.2.a.cb	$1$	$0$	\(-4\)	\(4\)	\(4\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5082.2.a.cc	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.8000.1	None	✓		✓		462.2.j.f	$1$	$0$	\(4\)	\(-4\)	\(2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cd	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.28400.1	None	✓		✓		462.2.j.h	$1$	$0$	\(4\)	\(-4\)	\(4\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
5082.2.a.ce	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	\(\Q(\sqrt{3}, \sqrt{5})\)	None	✓		✓		462.2.j.g	$1$	$0$	\(4\)	\(4\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{6}+\cdots\)
5082.2.a.cf	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.4400.1	None	✓				462.2.j.e	$1$	$0$	\(4\)	\(4\)	\(2\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cg	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.69264.1	None	✓	✓			5082.2.a.cb	$1$	$0$	\(4\)	\(4\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5082))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5082)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)