Space of modular forms of level 5610, weight 2, and trivial character

• Label: 5610.2.a
• Level: $5610$
• Weight: $2$
• Character orbit: 5610.a
• Rep. character: $\chi_{5610}(1,\cdot)$
• Character field: $\Q$
• Dimension: $111$
• Newform subspaces: $63$
• Sturm bound: $2592$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 63 \)
Sturm bound:			\(2592\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5610))\).

	Total	New	Old
Modular forms	1312	111	1201
Cusp forms	1281	111	1170
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(5\)	\(11\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
Plus space					\(+\)	\(44\)
Minus space					\(-\)	\(67\)

Trace form

111 * q - q^2 + 7 * q^3 + 111 * q^4 - q^5 - q^6 + 8 * q^7 - q^8 + 111 * q^9 - q^10 - q^11 + 7 * q^12 + 2 * q^13 - 8 * q^14 - q^15 + 111 * q^16 - q^17 - q^18 - 4 * q^19 - q^20 + 8 * q^21 + 7 * q^22 - 8 * q^23 - q^24 + 111 * q^25 + 2 * q^26 + 7 * q^27 + 8 * q^28 - 30 * q^29 - q^30 - q^32 - q^33 - q^34 - 8 * q^35 + 111 * q^36 + 26 * q^37 + 28 * q^38 + 34 * q^39 - q^40 + 22 * q^41 - 8 * q^42 + 36 * q^43 - q^44 - q^45 + 8 * q^46 + 16 * q^47 + 7 * q^48 + 119 * q^49 - q^50 - q^51 + 2 * q^52 + 26 * q^53 - q^54 - q^55 - 8 * q^56 + 28 * q^57 + 2 * q^58 + 20 * q^59 - q^60 + 18 * q^61 + 32 * q^62 + 8 * q^63 + 111 * q^64 + 18 * q^65 - q^66 + 60 * q^67 - q^68 + 8 * q^69 - 8 * q^70 + 8 * q^71 - q^72 + 6 * q^73 - 6 * q^74 + 7 * q^75 - 4 * q^76 + 8 * q^77 + 2 * q^78 + 64 * q^79 - q^80 + 111 * q^81 + 22 * q^82 + 44 * q^83 + 8 * q^84 - q^85 + 68 * q^86 + 34 * q^87 + 7 * q^88 - 26 * q^89 - q^90 - 16 * q^91 - 8 * q^92 + 16 * q^93 + 16 * q^94 - 20 * q^95 - q^96 + 30 * q^97 + 71 * q^98 - q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\) 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	5	11	17
5610.2.a.a	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.b	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.c	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.c	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.d	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.d	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
5610.2.a.e	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.f	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.f	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
5610.2.a.g	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.g	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.h	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.h	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.i	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.i	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
5610.2.a.j	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.j	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
5610.2.a.k	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.k	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.l	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.l	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.m	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.m	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.n	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.n	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.o	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.o	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.p	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.p	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(3\)		$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.q	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.q	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.r	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.r	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.s	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.s	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.t	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.t	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.u	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.u	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.v	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.v	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.w	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.w	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.x	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.x	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.y	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.y	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.z	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.z	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.ba	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.ba	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.bb	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓	✓	✓	5610.2.a.bb	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.bc	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bc	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bd	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bd	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.be	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.be	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bf	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bf	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bg	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bg	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
5610.2.a.bh	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bh	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bi	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bi	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.bj	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓			5610.2.a.bj	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(5\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+5q^{7}+\cdots\)
5610.2.a.bk	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓	✓	✓	5610.2.a.bk	$1$	$1$	\(1\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bl	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	\(\Q\)	None	✓	✓	✓	✓	5610.2.a.bl	$1$	$1$	\(1\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.bm	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{17}) \)	None	✓	✓			5610.2.a.bm	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bn	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	5610.2.a.bn	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bo	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{41}) \)	None	✓	✓	✓		5610.2.a.bo	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bp	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{33}) \)	None	✓	✓			5610.2.a.bp	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.bq	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{33}) \)	None	✓	✓			5610.2.a.bq	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.br	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{5}) \)	None	✓	✓			5610.2.a.br	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bs	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓		5610.2.a.bs	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bt	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	5610.2.a.bt	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bu	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		5610.2.a.bu	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bv	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{41}) \)	None	✓	✓	✓		5610.2.a.bv	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(-3\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bw	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		5610.2.a.bw	$1$	$1$	\(2\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bx	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	\(\Q(\sqrt{33}) \)	None	✓	✓			5610.2.a.bx	$1$	$0$	\(2\)	\(2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.by	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		5610.2.a.by	$1$	$0$	\(-3\)	\(3\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.bz	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.148.1	None	✓	✓	✓		5610.2.a.bz	$1$	$1$	\(-3\)	\(3\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.ca	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.961.1	None	✓	✓	✓		5610.2.a.ca	$1$	$0$	\(-3\)	\(3\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.cb	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.2089.1	None	✓	✓	✓		5610.2.a.cb	$1$	$0$	\(-3\)	\(3\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.cc	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓	✓	5610.2.a.cc	$1$	$1$	\(3\)	\(-3\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.cd	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.2089.1	None	✓	✓	✓		5610.2.a.cd	$1$	$0$	\(3\)	\(3\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ce	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.2777.1	None	✓	✓	✓	✓	5610.2.a.ce	$1$	$1$	\(-4\)	\(-4\)	\(4\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)
5610.2.a.cf	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.17428.1	None	✓	✓	✓	✓	5610.2.a.cf	$1$	$0$	\(-4\)	\(4\)	\(-4\)	\(5\)		$+$	$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
5610.2.a.cg	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.54764.1	None	✓	✓	✓		5610.2.a.cg	$1$	$0$	\(4\)	\(-4\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.ch	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.65905.1	None	✓	✓	✓		5610.2.a.ch	$1$	$0$	\(4\)	\(4\)	\(-4\)	\(1\)		$-$	$-$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ci	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.18569692.1	None	✓	✓	✓	✓	5610.2.a.ci	$1$	$0$	\(5\)	\(-5\)	\(5\)	\(2\)		$-$	$+$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-\beta _{3}q^{7}+\cdots\)
5610.2.a.cj	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.1284160.1	None	✓	✓	✓		5610.2.a.cj	$1$	$0$	\(5\)	\(5\)	\(5\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.ck	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.19985813.1	None	✓	✓	✓	✓	5610.2.a.ck	$1$	$0$	\(5\)	\(5\)	\(5\)	\(2\)		$-$	$-$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5610)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\)\(^{\oplus 2}\)