Space of modular forms of level 7104, weight 2, and trivial character

• Label: 7104.2.a
• Level: $7104$
• Weight: $2$
• Character orbit: 7104.a
• Rep. character: $\chi_{7104}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $64$
• Sturm bound: $2432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7104 = 2^{6} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7104.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 64 \)
Sturm bound:			\(2432\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7104))\).

	Total	New	Old
Modular forms	1240	144	1096
Cusp forms	1193	144	1049
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.

\(2\)	\(3\)	\(37\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(146\)	\(17\)	\(129\)		\(141\)	\(17\)	\(124\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(162\)	\(19\)	\(143\)		\(156\)	\(19\)	\(137\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(164\)	\(21\)	\(143\)		\(158\)	\(21\)	\(137\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(148\)	\(15\)	\(133\)		\(142\)	\(15\)	\(127\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(156\)	\(19\)	\(137\)		\(150\)	\(19\)	\(131\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(156\)	\(17\)	\(139\)		\(150\)	\(17\)	\(133\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(154\)	\(15\)	\(139\)		\(148\)	\(15\)	\(133\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(154\)	\(21\)	\(133\)		\(148\)	\(21\)	\(127\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(604\)	\(64\)	\(540\)		\(581\)	\(64\)	\(517\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(636\)	\(80\)	\(556\)		\(612\)	\(80\)	\(532\)		\(24\)	\(0\)	\(24\)

Trace form

\( 144 q + 144 q^{9} + 144 q^{25} + 144 q^{49} + 32 q^{61} + 32 q^{69} - 96 q^{77} + 144 q^{81} - 64 q^{85} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7104))\) 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	37
7104.2.a.a	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
7104.2.a.b	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}-2q^{13}+4q^{15}+\cdots\)
7104.2.a.c	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
7104.2.a.d	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7104.2.a.e	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7104.2.a.f	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}+q^{11}-q^{13}-3q^{17}+\cdots\)
7104.2.a.g	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}-3q^{17}+\cdots\)
7104.2.a.h	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+6q^{13}-4q^{17}+4q^{19}+\cdots\)
7104.2.a.i	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				444.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{11}+2q^{13}+6q^{19}+\cdots\)
7104.2.a.j	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
7104.2.a.k	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				444.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
7104.2.a.l	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7104.2.a.m	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
7104.2.a.n	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
7104.2.a.o	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}-2q^{13}-4q^{15}+\cdots\)
7104.2.a.p	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
7104.2.a.q	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
7104.2.a.r	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
7104.2.a.s	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				444.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}+2q^{13}-6q^{19}+\cdots\)
7104.2.a.t	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
7104.2.a.u	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+3q^{11}+q^{13}-3q^{17}+\cdots\)
7104.2.a.v	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-q^{11}-q^{13}-3q^{17}+\cdots\)
7104.2.a.w	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7104.2.a.x	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				3552.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7104.2.a.y	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.c	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7104.2.a.z	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				444.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
7104.2.a.ba	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				888.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
7104.2.a.bb	$7104$	$2$	7104.a	1.a	$1$	$1$	$1$	$56.726$	\(\Q\)	None	✓				222.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
7104.2.a.bc	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{5}) \)	None	✓				888.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-8\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-4q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
7104.2.a.bd	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{3}) \)	None	✓				888.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+2q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7104.2.a.be	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{41}) \)	None	✓				888.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
7104.2.a.bf	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{6}) \)	None	✓				444.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+2q^{7}+q^{9}+(-2-2\beta )q^{13}+\cdots\)
7104.2.a.bg	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{3}) \)	None	✓				444.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}-4q^{11}+\cdots\)
7104.2.a.bh	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{2}) \)	None	✓				888.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
7104.2.a.bi	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{3}) \)	None	✓				888.2.a.e	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}-2q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
7104.2.a.bj	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{5}) \)	None	✓				888.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(8\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+4q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7104.2.a.bk	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{6}) \)	None	✓				444.2.a.d	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-2q^{7}+q^{9}+(-2-2\beta )q^{13}+\cdots\)
7104.2.a.bl	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{41}) \)	None	✓				888.2.a.h	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
7104.2.a.bm	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{3}) \)	None	✓				444.2.a.c	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+4q^{11}+\cdots\)
7104.2.a.bn	$7104$	$2$	7104.a	1.a	$1$	$2$	$2$	$56.726$	\(\Q(\sqrt{2}) \)	None	✓				888.2.a.g	$1$	$0$	\(0\)	\(2\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
7104.2.a.bo	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.i	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+2\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
7104.2.a.bp	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				111.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
7104.2.a.bq	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.316.1	None	✓				888.2.a.i	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots\)
7104.2.a.br	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.568.1	None	✓				888.2.a.j	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)
7104.2.a.bs	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.h	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
7104.2.a.bt	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
7104.2.a.bu	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				111.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
7104.2.a.bv	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.i	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+2\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7104.2.a.bw	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.316.1	None	✓				888.2.a.i	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
7104.2.a.bx	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.568.1	None	✓				888.2.a.j	$1$	$0$	\(0\)	\(3\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
7104.2.a.by	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.g	$1$	$1$	\(0\)	\(3\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7104.2.a.bz	$7104$	$2$	7104.a	1.a	$1$	$3$	$3$	$56.726$	3.3.148.1	None	✓				3552.2.a.h	$1$	$0$	\(0\)	\(3\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
7104.2.a.ca	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.15188.1	None	✓				3552.2.a.o	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+\cdots\)
7104.2.a.cb	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.11348.1	None	✓				3552.2.a.n	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
7104.2.a.cc	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.6224.1	None	✓				111.2.a.b	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{3})q^{5}+(2-\beta _{2}-\beta _{3})q^{7}+\cdots\)
7104.2.a.cd	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.97300.1	None	✓		✓		3552.2.a.m	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7104.2.a.ce	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.15188.1	None	✓				3552.2.a.o	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
7104.2.a.cf	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.6224.1	None	✓				111.2.a.b	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
7104.2.a.cg	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.11348.1	None	✓				3552.2.a.n	$1$	$1$	\(0\)	\(4\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
7104.2.a.ch	$7104$	$2$	7104.a	1.a	$1$	$4$	$4$	$56.726$	4.4.97300.1	None	✓				3552.2.a.m	$1$	$0$	\(0\)	\(4\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7104.2.a.ci	$7104$	$2$	7104.a	1.a	$1$	$5$	$5$	$56.726$	5.5.792644.1	None	✓		✓		3552.2.a.s	$1$	$0$	\(0\)	\(-5\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7104.2.a.cj	$7104$	$2$	7104.a	1.a	$1$	$5$	$5$	$56.726$	5.5.792644.1	None	✓		✓		3552.2.a.s	$1$	$1$	\(0\)	\(5\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7104.2.a.ck	$7104$	$2$	7104.a	1.a	$1$	$7$	$7$	$56.726$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		3552.2.a.u	$1$	$1$	\(0\)	\(-7\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7104.2.a.cl	$7104$	$2$	7104.a	1.a	$1$	$7$	$7$	$56.726$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		3552.2.a.u	$1$	$0$	\(0\)	\(7\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7104)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3552))\)\(^{\oplus 2}\)