Space of modular forms of level 7616, weight 2, and trivial character

• Label: 7616.2.a
• Level: $7616$
• Weight: $2$
• Character orbit: 7616.a
• Rep. character: $\chi_{7616}(1,\cdot)$
• Character field: $\Q$
• Dimension: $192$
• Newform subspaces: $58$
• Sturm bound: $2304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7616 = 2^{6} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7616.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2304\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7616))\).

	Total	New	Old
Modular forms	1176	192	984
Cusp forms	1129	192	937
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.

\(2\)	\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(22\)
\(+\)	\(+\)	\(-\)	\(-\)	\(27\)
\(+\)	\(-\)	\(+\)	\(-\)	\(26\)
\(+\)	\(-\)	\(-\)	\(+\)	\(21\)
\(-\)	\(+\)	\(+\)	\(-\)	\(26\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)	\(27\)
Plus space			\(+\)	\(86\)
Minus space			\(-\)	\(106\)

Trace form

\( 192 q + 192 q^{9} + 192 q^{25} + 16 q^{29} + 16 q^{37} - 96 q^{45} + 192 q^{49} - 80 q^{53} - 96 q^{69} + 16 q^{77} + 192 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7616))\) 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	7	17
7616.2.a.a	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{5}+q^{7}+q^{9}+4q^{11}+\cdots\)
7616.2.a.b	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				3808.2.a.a	$1$	$2$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
7616.2.a.c	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
7616.2.a.d	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
7616.2.a.e	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
7616.2.a.f	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
7616.2.a.g	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots\)
7616.2.a.h	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-3q^{9}-2q^{11}-q^{17}+\cdots\)
7616.2.a.i	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
7616.2.a.j	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.e	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7616.2.a.k	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				3808.2.a.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots\)
7616.2.a.l	$7616$	$2$	7616.a	1.a	$1$	$1$	$1$	$60.814$	\(\Q\)	None	✓				238.2.a.c	$1$	$0$	\(0\)	\(2\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
7616.2.a.m	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
7616.2.a.n	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				238.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
7616.2.a.o	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
7616.2.a.p	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				476.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.q	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}+(-4+\cdots)q^{13}+\cdots\)
7616.2.a.r	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				952.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.s	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				952.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}-q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
7616.2.a.t	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
7616.2.a.u	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				476.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.v	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(-4+\cdots)q^{13}+\cdots\)
7616.2.a.w	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				952.2.a.a	$1$	$1$	\(0\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.x	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				952.2.a.b	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{5}+q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
7616.2.a.y	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{5}) \)	None	✓				238.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
7616.2.a.z	$7616$	$2$	7616.a	1.a	$1$	$2$	$2$	$60.814$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.a	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-\beta )q^{5}+q^{7}+(1+3\beta )q^{9}+\cdots\)
7616.2.a.ba	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bb	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.c	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(2+\beta _{2})q^{5}-q^{7}+\cdots\)
7616.2.a.bc	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bd	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.1229.1	None	✓				952.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7616.2.a.be	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bf	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.1229.1	None	✓				952.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7616.2.a.bg	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.d	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bh	$7616$	$2$	7616.a	1.a	$1$	$3$	$3$	$60.814$	3.3.229.1	None	✓				952.2.a.c	$1$	$0$	\(0\)	\(3\)	\(5\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
7616.2.a.bi	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.13448.1	None	✓				952.2.a.h	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\cdots\)
7616.2.a.bj	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.5225.1	None	✓				952.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bk	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.9301.1	None	✓				119.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7616.2.a.bl	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	\(\Q(\zeta_{20})^+\)	None	✓				3808.2.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{1})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots\)
7616.2.a.bm	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	\(\Q(\zeta_{20})^+\)	None	✓				3808.2.a.c	$1$	$1$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
7616.2.a.bn	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.9301.1	None	✓				119.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7616.2.a.bo	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.13448.1	None	✓				952.2.a.h	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bp	$7616$	$2$	7616.a	1.a	$1$	$4$	$4$	$60.814$	4.4.5225.1	None	✓				952.2.a.g	$1$	$0$	\(0\)	\(3\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
7616.2.a.bq	$7616$	$2$	7616.a	1.a	$1$	$5$	$5$	$60.814$	5.5.453749.1	None	✓				119.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.br	$7616$	$2$	7616.a	1.a	$1$	$5$	$5$	$60.814$	5.5.804272.1	None	✓				3808.2.a.e	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bs	$7616$	$2$	7616.a	1.a	$1$	$5$	$5$	$60.814$	5.5.804272.1	None	✓				3808.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+q^{7}+\cdots\)
7616.2.a.bt	$7616$	$2$	7616.a	1.a	$1$	$5$	$5$	$60.814$	5.5.453749.1	None	✓				119.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-5\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.bu	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.109859312.1	None	✓		✓		3808.2.a.h	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{5})q^{3}+(-1+\beta _{1})q^{5}+q^{7}+\cdots\)
7616.2.a.bv	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.147697840.1	None	✓				3808.2.a.g	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-6\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1+\beta _{5})q^{5}-q^{7}+\cdots\)
7616.2.a.bw	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.4022000.1	None	✓				3808.2.a.j	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+\beta _{1}q^{5}+q^{7}+(1-\beta _{5})q^{9}+\cdots\)
7616.2.a.bx	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.80686992.1	None	✓				3808.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(6\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.by	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.93059344.1	None	✓				3808.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}-q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.bz	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.93059344.1	None	✓				3808.2.a.k	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.ca	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.4022000.1	None	✓				3808.2.a.j	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-6\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+\beta _{1}q^{5}-q^{7}+(1-\beta _{5})q^{9}+\cdots\)
7616.2.a.cb	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.80686992.1	None	✓				3808.2.a.i	$1$	$0$	\(0\)	\(2\)	\(6\)	\(6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.cc	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.109859312.1	None	✓		✓		3808.2.a.h	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{5})q^{3}+(-1+\beta _{1})q^{5}-q^{7}+\cdots\)
7616.2.a.cd	$7616$	$2$	7616.a	1.a	$1$	$6$	$6$	$60.814$	6.6.147697840.1	None	✓				3808.2.a.g	$1$	$0$	\(0\)	\(4\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1+\beta _{5})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
7616.2.a.ce	$7616$	$2$	7616.a	1.a	$1$	$8$	$8$	$60.814$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		3808.2.a.q	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(8\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+(-1-\beta _{5})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.cf	$7616$	$2$	7616.a	1.a	$1$	$8$	$8$	$60.814$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		3808.2.a.q	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(-8\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7616)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1904))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3808))\)\(^{\oplus 2}\)