Space of modular forms of level 7938, weight 2, and trivial character

• Label: 7938.2.a
• Level: $7938$
• Weight: $2$
• Character orbit: 7938.a
• Rep. character: $\chi_{7938}(1,\cdot)$
• Character field: $\Q$
• Dimension: $164$
• Newform subspaces: $74$
• Sturm bound: $3024$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7938.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 74 \)
Sturm bound:			\(3024\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7938))\).

	Total	New	Old
Modular forms	1608	164	1444
Cusp forms	1417	164	1253
Eisenstein series	191	0	191

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

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(194\)	\(20\)	\(174\)		\(171\)	\(20\)	\(151\)		\(23\)	\(0\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)		\(208\)	\(21\)	\(187\)		\(184\)	\(21\)	\(163\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(+\)	\(-\)		\(206\)	\(20\)	\(186\)		\(182\)	\(20\)	\(162\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)		\(196\)	\(21\)	\(175\)		\(172\)	\(21\)	\(151\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)		\(202\)	\(24\)	\(178\)		\(178\)	\(24\)	\(154\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)	\(+\)		\(200\)	\(18\)	\(182\)		\(176\)	\(18\)	\(158\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)		\(202\)	\(16\)	\(186\)		\(178\)	\(16\)	\(162\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)		\(200\)	\(24\)	\(176\)		\(176\)	\(24\)	\(152\)		\(24\)	\(0\)	\(24\)
Plus space			\(+\)		\(792\)	\(75\)	\(717\)		\(697\)	\(75\)	\(622\)		\(95\)	\(0\)	\(95\)
Minus space			\(-\)		\(816\)	\(89\)	\(727\)		\(720\)	\(89\)	\(631\)		\(96\)	\(0\)	\(96\)

Trace form

164 * q + 164 * q^4 + 6 * q^10 + 10 * q^13 + 164 * q^16 - 2 * q^19 - 6 * q^22 + 158 * q^25 - 8 * q^31 - 2 * q^37 + 6 * q^40 - 26 * q^43 + 12 * q^46 + 10 * q^52 - 24 * q^55 + 18 * q^58 - 2 * q^61 + 164 * q^64 - 38 * q^67 - 44 * q^73 - 2 * q^76 + 40 * q^79 + 6 * q^82 + 18 * q^85 - 6 * q^88 - 12 * q^94 + 22 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7938))\) 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
7938.2.a.a	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.a	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-2q^{11}+\cdots\)
7938.2.a.b	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{11}+\cdots\)
7938.2.a.c	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.b	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
7938.2.a.d	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+6q^{11}+\cdots\)
7938.2.a.e	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.f.b	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
7938.2.a.f	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				882.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
7938.2.a.g	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-4q^{13}+q^{16}-6q^{17}+\cdots\)
7938.2.a.h	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
7938.2.a.i	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				18.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+3q^{11}-2q^{13}+\cdots\)
7938.2.a.j	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
7938.2.a.k	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				882.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots\)
7938.2.a.l	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.f.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-6q^{11}+\cdots\)
7938.2.a.m	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.a	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-3q^{11}+\cdots\)
7938.2.a.n	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				162.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{13}+\cdots\)
7938.2.a.o	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.b	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
7938.2.a.p	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.a	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-q^{8}-4q^{10}-2q^{11}+\cdots\)
7938.2.a.q	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.a	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+2q^{11}+\cdots\)
7938.2.a.r	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.b	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
7938.2.a.s	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				162.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{13}+\cdots\)
7938.2.a.t	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.a	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+3q^{11}+\cdots\)
7938.2.a.u	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.f.a	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+6q^{11}+\cdots\)
7938.2.a.v	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				882.2.f.b	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{11}+\cdots\)
7938.2.a.w	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots\)
7938.2.a.x	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				18.2.c.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-3q^{11}-2q^{13}+\cdots\)
7938.2.a.y	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-4q^{13}+q^{16}+6q^{17}+\cdots\)
7938.2.a.z	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}-6q^{17}+\cdots\)
7938.2.a.ba	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				882.2.f.b	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{11}+\cdots\)
7938.2.a.bb	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.f.b	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
7938.2.a.bc	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.a.d	$1$	$1$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-6q^{11}+\cdots\)
7938.2.a.bd	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.b	$1$	$1$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
7938.2.a.be	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				126.2.e.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+3q^{11}+\cdots\)
7938.2.a.bf	$7938$	$2$	7938.a	1.a	$1$	$1$	$1$	$63.385$	\(\Q\)	None	✓				1134.2.g.a	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+2q^{11}+\cdots\)
7938.2.a.bg	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.l	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-2+\beta )q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
7938.2.a.bh	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{33}) \)	None	✓				126.2.f.d	$1$	$0$	\(-2\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
7938.2.a.bi	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.j	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(-3+\cdots)q^{11}+\cdots\)
7938.2.a.bj	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{2}) \)	None	✓				1134.2.g.i	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
7938.2.a.bk	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{2}) \)	None	✓				1134.2.g.i	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+\beta q^{11}+(2-\beta )q^{13}+\cdots\)
7938.2.a.bl	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{7}) \)	None	✓	✓			7938.2.a.bl	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+2q^{11}+\cdots\)
7938.2.a.bm	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{6}) \)	None	✓				126.2.f.c	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.bn	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{6}) \)	None	✓				126.2.f.c	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.bo	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{7}) \)	None	✓	✓			7938.2.a.bl	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-2q^{11}+\cdots\)
7938.2.a.bp	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{2}) \)	None	✓				1134.2.g.i	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
7938.2.a.bq	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{2}) \)	None	✓				1134.2.g.i	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+\beta q^{11}+(2+\beta )q^{13}+\cdots\)
7938.2.a.br	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.j	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(3+\cdots)q^{11}+\cdots\)
7938.2.a.bs	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{33}) \)	None	✓				126.2.f.d	$1$	$0$	\(2\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
7938.2.a.bt	$7938$	$2$	7938.a	1.a	$1$	$2$	$2$	$63.385$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.l	$1$	$0$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(2+\beta )q^{5}+q^{8}+(2+\beta )q^{10}+\cdots\)
7938.2.a.bu	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.d	$1$	$0$	\(-3\)	\(0\)	\(-5\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
7938.2.a.bv	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.c	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{8}-\beta _{2}q^{10}+\cdots\)
7938.2.a.bw	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.c	$1$	$0$	\(-3\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+\beta _{2}q^{10}+\cdots\)
7938.2.a.bx	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.d	$1$	$1$	\(-3\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2-\beta _{1})q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
7938.2.a.by	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓		✓		126.2.e.d	$1$	$1$	\(3\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}+q^{8}+(-2+\cdots)q^{10}+\cdots\)
7938.2.a.bz	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.c	$1$	$0$	\(3\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
7938.2.a.ca	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.c	$1$	$1$	\(3\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{2}q^{5}+q^{8}-\beta _{2}q^{10}+\cdots\)
7938.2.a.cb	$7938$	$2$	7938.a	1.a	$1$	$3$	$3$	$63.385$	3.3.321.1	None	✓				126.2.e.d	$1$	$0$	\(3\)	\(0\)	\(5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+q^{8}+(2-\beta _{1}+\cdots)q^{10}+\cdots\)
7938.2.a.cc	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓				1134.2.g.o	$1$	$1$	\(-4\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{3})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
7938.2.a.cd	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓				882.2.f.p	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ce	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓	✓			7938.2.a.ce	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.cf	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓	✓			7938.2.a.cf	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{8}-\beta _{3}q^{10}+\cdots\)
7938.2.a.cg	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓	✓			7938.2.a.cg	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ch	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{7}, \sqrt{15})\)	None	✓		✓		882.2.f.r	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{8}-\beta _{3}q^{10}+\cdots\)
7938.2.a.ci	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓				882.2.f.q	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta _{1}q^{5}-q^{8}-2\beta _{1}q^{10}+\cdots\)
7938.2.a.cj	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓				882.2.f.s	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ck	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7938.2.a.ck	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.cl	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓				1134.2.g.o	$1$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta _{3})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.cm	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓				1134.2.g.o	$1$	$1$	\(4\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta _{3})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.cn	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7938.2.a.ck	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.co	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓				882.2.f.s	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cp	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\zeta_{24})^+\)	None	✓				882.2.f.q	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2\beta _{1}q^{5}+q^{8}+2\beta _{1}q^{10}+\cdots\)
7938.2.a.cq	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{7}, \sqrt{15})\)	None	✓				882.2.f.r	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{3}q^{5}+q^{8}+\beta _{3}q^{10}+\cdots\)
7938.2.a.cr	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓	✓			7938.2.a.cg	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cs	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓	✓			7938.2.a.cf	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{3}q^{5}+q^{8}+\beta _{3}q^{10}+\cdots\)
7938.2.a.ct	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓	✓			7938.2.a.ce	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cu	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	\(\Q(\sqrt{2}, \sqrt{15})\)	None	✓				882.2.f.p	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cv	$7938$	$2$	7938.a	1.a	$1$	$4$	$4$	$63.385$	4.4.21312.1	None	✓				1134.2.g.o	$1$	$0$	\(4\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{3})q^{5}+q^{8}+(1+\beta _{3})q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7938))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7938)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3969))\)\(^{\oplus 2}\)