Space of modular forms of level 5712, weight 2, and trivial character

• Label: 5712.2.a
• Level: $5712$
• Weight: $2$
• Character orbit: 5712.a
• Rep. character: $\chi_{5712}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $54$
• Sturm bound: $2304$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5712 = 2^{4} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5712.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 54 \)
Sturm bound:			\(2304\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5712))\).

	Total	New	Old
Modular forms	1176	96	1080
Cusp forms	1129	96	1033
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.

\(2\)	\(3\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(62\)	\(7\)	\(55\)		\(60\)	\(7\)	\(53\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(83\)	\(5\)	\(78\)		\(80\)	\(5\)	\(75\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(81\)	\(8\)	\(73\)		\(78\)	\(8\)	\(70\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(68\)	\(4\)	\(64\)		\(65\)	\(4\)	\(61\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(66\)	\(5\)	\(61\)		\(63\)	\(5\)	\(58\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(83\)	\(7\)	\(76\)		\(80\)	\(7\)	\(73\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(77\)	\(4\)	\(73\)		\(74\)	\(4\)	\(70\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(68\)	\(8\)	\(60\)		\(65\)	\(8\)	\(57\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(75\)	\(7\)	\(68\)		\(72\)	\(7\)	\(65\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(74\)	\(6\)	\(68\)		\(71\)	\(6\)	\(65\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(76\)	\(5\)	\(71\)		\(73\)	\(5\)	\(68\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(69\)	\(6\)	\(63\)		\(66\)	\(6\)	\(60\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(71\)	\(6\)	\(65\)		\(68\)	\(6\)	\(62\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(74\)	\(7\)	\(67\)		\(71\)	\(7\)	\(64\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(80\)	\(6\)	\(74\)		\(77\)	\(6\)	\(71\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(69\)	\(5\)	\(64\)		\(66\)	\(5\)	\(61\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(580\)	\(44\)	\(536\)		\(557\)	\(44\)	\(513\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(596\)	\(52\)	\(544\)		\(572\)	\(52\)	\(520\)		\(24\)	\(0\)	\(24\)

Trace form

96 * q - 4 * q^7 + 96 * q^9 - 8 * q^11 - 8 * q^23 + 96 * q^25 + 16 * q^29 + 16 * q^37 - 16 * q^39 - 40 * q^43 + 96 * q^49 + 12 * q^51 + 16 * q^53 - 8 * q^55 - 4 * q^63 + 16 * q^67 - 8 * q^71 - 32 * q^75 + 16 * q^77 - 48 * q^79 + 96 * q^81 - 80 * q^83 + 24 * q^87 - 32 * q^89 + 24 * q^91 - 32 * q^95 - 32 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5712))\) 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	17
5712.2.a.a	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
5712.2.a.b	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				1428.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
5712.2.a.c	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				357.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
5712.2.a.d	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.e	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
5712.2.a.e	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
5712.2.a.f	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
5712.2.a.g	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
5712.2.a.h	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
5712.2.a.i	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				357.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
5712.2.a.j	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
5712.2.a.k	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				1428.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
5712.2.a.l	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
5712.2.a.m	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}-5q^{11}-3q^{13}+\cdots\)
5712.2.a.n	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				1428.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
5712.2.a.o	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5712.2.a.p	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
5712.2.a.q	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
5712.2.a.r	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
5712.2.a.s	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
5712.2.a.t	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				1428.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-7q^{13}+\cdots\)
5712.2.a.u	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				357.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
5712.2.a.v	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
5712.2.a.w	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				357.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots\)
5712.2.a.x	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				2856.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5712.2.a.y	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				1428.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots\)
5712.2.a.z	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}+2q^{15}+\cdots\)
5712.2.a.ba	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.h	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
5712.2.a.bb	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	\(\Q\)	None	✓				714.2.a.g	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
5712.2.a.bc	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{3}) \)	None	✓				357.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}+5q^{11}+\cdots\)
5712.2.a.bd	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{33}) \)	None	✓				714.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5712.2.a.be	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{17}) \)	None	✓				2856.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
5712.2.a.bf	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{2}) \)	None	✓				1428.2.a.g	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5712.2.a.bg	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{3}) \)	None	✓				2856.2.a.o	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(3+2\beta )q^{11}+\cdots\)
5712.2.a.bh	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{15}) \)	None	✓				2856.2.a.n	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+5q^{11}+(2+\cdots)q^{13}+\cdots\)
5712.2.a.bi	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{41}) \)	None	✓				714.2.a.k	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
5712.2.a.bj	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{10}) \)	None	✓				1428.2.a.h	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
5712.2.a.bk	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{17}) \)	None	✓				1428.2.a.i	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5712.2.a.bl	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{17}) \)	None	✓				714.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5712.2.a.bm	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{6}) \)	None	✓				714.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
5712.2.a.bn	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{201}) \)	None	✓		✓		2856.2.a.p	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
5712.2.a.bo	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{3}) \)	None	✓		✓		1428.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
5712.2.a.bp	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{17}) \)	None	✓				2856.2.a.k	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
5712.2.a.bq	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{2}) \)	None	✓		✓		357.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
5712.2.a.br	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	\(\Q(\sqrt{17}) \)	None	✓				2856.2.a.l	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+(1-2\beta )q^{11}+\cdots\)
5712.2.a.bs	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.316.1	None	✓		✓		2856.2.a.s	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+q^{7}+q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
5712.2.a.bt	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.316.1	None	✓		✓		357.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
5712.2.a.bu	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.568.1	None	✓				2856.2.a.q	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}-q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5712.2.a.bv	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.961.1	None	✓		✓		2856.2.a.r	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5712.2.a.bw	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.4764.1	None	✓		✓		1428.2.a.j	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
5712.2.a.bx	$5712$	$2$	5712.a	1.a	$1$	$4$	$4$	$45.611$	4.4.7232.1	None	✓		✓		357.2.a.h	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
5712.2.a.by	$5712$	$2$	5712.a	1.a	$1$	$4$	$4$	$45.611$	4.4.81416.1	None	✓		✓		2856.2.a.t	$1$	$1$	\(0\)	\(4\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+\beta _{3})q^{11}+\cdots\)
5712.2.a.bz	$5712$	$2$	5712.a	1.a	$1$	$4$	$4$	$45.611$	4.4.7232.1	None	✓				2856.2.a.u	$1$	$0$	\(0\)	\(4\)	\(2\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{3}q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
5712.2.a.ca	$5712$	$2$	5712.a	1.a	$1$	$4$	$4$	$45.611$	4.4.183064.1	None	✓				2856.2.a.v	$1$	$0$	\(0\)	\(4\)	\(5\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
5712.2.a.cb	$5712$	$2$	5712.a	1.a	$1$	$5$	$5$	$45.611$	5.5.14050576.1	None	✓		✓		2856.2.a.w	$1$	$1$	\(0\)	\(-5\)	\(1\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+(-\beta _{2}-\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5712))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5712)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1428))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1904))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2856))\)\(^{\oplus 2}\)