Space of modular forms of level 7744, weight 2, and trivial character

• Label: 7744.2.a
• Level: $7744$
• Weight: $2$
• Character orbit: 7744.a
• Rep. character: $\chi_{7744}(1,\cdot)$
• Character field: $\Q$
• Dimension: $209$
• Newform subspaces: $101$
• Sturm bound: $2112$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7744 = 2^{6} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7744.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 101 \)
Sturm bound:			\(2112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7744))\).

	Total	New	Old
Modular forms	1128	227	901
Cusp forms	985	209	776
Eisenstein series	143	18	125

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

\(2\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(49\)
\(+\)	\(-\)	$-$	\(55\)
\(-\)	\(+\)	$-$	\(55\)
\(-\)	\(-\)	$+$	\(50\)
Plus space		\(+\)	\(99\)
Minus space		\(-\)	\(110\)

Trace form

\( 209 q - 2 q^{5} + 193 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7744))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	11
7744.2.a.a	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+6q^{9}-6q^{13}+3q^{15}+\cdots\)
7744.2.a.b	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+3q^{5}-2q^{7}+6q^{9}-9q^{15}+\cdots\)
7744.2.a.c	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
7744.2.a.d	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
7744.2.a.e	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
7744.2.a.f	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
7744.2.a.g	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots\)
7744.2.a.h	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots\)
7744.2.a.i	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.j	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.k	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.l	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.m	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.n	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-q^{3}+3q^{5}-2q^{9}-3q^{15}+9q^{23}+\cdots\)
7744.2.a.o	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.p	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}-3q^{9}-3q^{13}+3q^{17}+\cdots\)
7744.2.a.q	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}-3q^{9}+3q^{13}-3q^{17}+\cdots\)
7744.2.a.r	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-3q^{9}-3q^{13}+3q^{17}+\cdots\)
7744.2.a.s	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-3q^{9}+3q^{13}-3q^{17}+\cdots\)
7744.2.a.t	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}-3q^{9}-4q^{13}-8q^{17}-q^{25}+\cdots\)
7744.2.a.u	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}-3q^{9}+4q^{13}+8q^{17}-q^{25}+\cdots\)
7744.2.a.v	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+2q^{5}-3q^{9}+6q^{13}-2q^{17}-q^{25}+\cdots\)
7744.2.a.w	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.x	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.y	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.z	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.ba	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.bb	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$1$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+q^{3}+3q^{5}-2q^{9}+3q^{15}-9q^{23}+\cdots\)
7744.2.a.bc	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+2q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.bd	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7744.2.a.be	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7744.2.a.bf	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7744.2.a.bg	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7744.2.a.bh	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}-2q^{7}+q^{9}+5q^{13}+\cdots\)
7744.2.a.bi	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}+2q^{7}+q^{9}-5q^{13}+\cdots\)
7744.2.a.bj	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}-6q^{13}-3q^{15}+\cdots\)
7744.2.a.bk	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots\)
7744.2.a.bl	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(-4\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{5}-2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots\)
7744.2.a.bm	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}-2q^{7}+\cdots\)
7744.2.a.bn	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots\)
7744.2.a.bo	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}+(1-3\beta )q^{7}+\cdots\)
7744.2.a.bp	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
7744.2.a.bq	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
7744.2.a.br	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-\beta q^{5}+(-1-\beta )q^{7}+\cdots\)
7744.2.a.bs	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-\beta q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7744.2.a.bt	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7744.2.a.bu	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
7744.2.a.bv	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
7744.2.a.bw	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots\)
7744.2.a.bx	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-\beta q^{3}+(-2+\beta )q^{5}+(5+\beta )q^{9}+(-8+\cdots)q^{15}+\cdots\)
7744.2.a.by	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
7744.2.a.bz	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.ca	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cb	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cc	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cd	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}-2q^{7}+2q^{9}+2\beta q^{13}+\cdots\)
7744.2.a.ce	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+(-1+\beta )q^{5}-3q^{9}+(-3+\beta )q^{13}+\cdots\)
7744.2.a.cf	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+(-1+\beta )q^{5}-3q^{9}+(3-\beta )q^{13}+\cdots\)
7744.2.a.cg	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+2q^{7}+2q^{9}-2\beta q^{13}+\cdots\)
7744.2.a.ch	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(1-2\beta )q^{5}-3q^{9}+(-2-3\beta )q^{13}+\cdots\)
7744.2.a.ci	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(1-2\beta )q^{5}-3q^{9}+(2+3\beta )q^{13}+\cdots\)
7744.2.a.cj	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+3q^{5}-2\beta q^{7}+2q^{9}-6q^{13}+\cdots\)
7744.2.a.ck	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+3q^{5}+2\beta q^{7}+2q^{9}+6q^{13}+\cdots\)
7744.2.a.cl	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
7744.2.a.cm	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots\)
7744.2.a.cn	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{3}+(-2+\beta )q^{5}+(5+\beta )q^{9}+(8+\cdots)q^{15}+\cdots\)
7744.2.a.co	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cp	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cq	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cr	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cs	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7744.2.a.ct	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7744.2.a.cu	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
7744.2.a.cv	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
7744.2.a.cw	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
7744.2.a.cx	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
7744.2.a.cy	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}-2q^{7}+\cdots\)
7744.2.a.cz	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots\)
7744.2.a.da	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}+(1-3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots\)
7744.2.a.db	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
7744.2.a.dc	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(4\)	\(-6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-2\beta q^{7}+q^{9}+3\beta q^{13}+\cdots\)
7744.2.a.dd	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7744.2.a.de	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7744.2.a.df	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7744.2.a.dg	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7744.2.a.dh	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
7744.2.a.di	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7744.2.a.dj	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-8\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
7744.2.a.dk	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(8\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+\cdots\)
7744.2.a.dl	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.22000.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-2-3\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
7744.2.a.dm	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.22000.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-2-3\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
7744.2.a.dn	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.7488.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots\)
7744.2.a.do	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.7488.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots\)
7744.2.a.dp	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.4400.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7744.2.a.dq	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.4400.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7744.2.a.dr	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
7744.2.a.ds	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7744.2.a.dt	$7744$	$2$	7744.a	1.a	$1$	$6$	$6$	$61.836$	6.6.19898000.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7744.2.a.du	$7744$	$2$	7744.a	1.a	$1$	$6$	$6$	$61.836$	6.6.19898000.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7744.2.a.dv	$7744$	$2$	7744.a	1.a	$1$	$6$	$6$	$61.836$	6.6.19898000.1	None	✓	$1$	$1$	\(0\)	\(5\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7744.2.a.dw	$7744$	$2$	7744.a	1.a	$1$	$6$	$6$	$61.836$	6.6.19898000.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3872))\)\(^{\oplus 2}\)