Space of modular forms of level 9248, weight 2, and trivial character

• Label: 9248.2.a
• Level: $9248$
• Weight: $2$
• Character orbit: 9248.a
• Rep. character: $\chi_{9248}(1,\cdot)$
• Character field: $\Q$
• Dimension: $271$
• Newform subspaces: $52$
• Sturm bound: $2448$
• Trace bound: $145$

Defining parameters

Level:	\( N \)	\(=\)	\( 9248 = 2^{5} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9248.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(2448\)
Trace bound:			\(145\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9248))\).

	Total	New	Old
Modular forms	1296	271	1025
Cusp forms	1153	271	882
Eisenstein series	143	0	143

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

\(2\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(315\)	\(64\)	\(251\)		\(280\)	\(64\)	\(216\)		\(35\)	\(0\)	\(35\)
\(+\)	\(-\)	\(-\)		\(331\)	\(72\)	\(259\)		\(295\)	\(72\)	\(223\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(-\)		\(333\)	\(71\)	\(262\)		\(297\)	\(71\)	\(226\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(+\)		\(317\)	\(64\)	\(253\)		\(281\)	\(64\)	\(217\)		\(36\)	\(0\)	\(36\)
Plus space		\(+\)		\(632\)	\(128\)	\(504\)		\(561\)	\(128\)	\(433\)		\(71\)	\(0\)	\(71\)
Minus space		\(-\)		\(664\)	\(143\)	\(521\)		\(592\)	\(143\)	\(449\)		\(72\)	\(0\)	\(72\)

Trace form

271 * q + 2 * q^5 + 275 * q^9 + 10 * q^13 + 257 * q^25 - 6 * q^29 - 16 * q^33 + 18 * q^37 - 26 * q^41 + 26 * q^45 + 263 * q^49 + 34 * q^53 - 16 * q^57 + 26 * q^61 - 36 * q^65 + 32 * q^69 + 6 * q^73 + 279 * q^81 + 6 * q^89 + 64 * q^93 + 30 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9248))\) 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	17
9248.2.a.a	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
9248.2.a.b	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
9248.2.a.c	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				544.2.b.a	$2$	$2$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-4q^{5}-3q^{9}-6q^{13}+11q^{25}-4q^{29}+\cdots\)
9248.2.a.d	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-4q^{11}+2q^{13}+4q^{19}+\cdots\)
9248.2.a.e	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-4q^{19}+\cdots\)
9248.2.a.f	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				32.2.a.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+2q^{5}-3q^{9}+6q^{13}-q^{25}+10q^{29}+\cdots\)
9248.2.a.g	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				544.2.b.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{5}-3q^{9}-6q^{13}+11q^{25}+4q^{29}+\cdots\)
9248.2.a.h	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
9248.2.a.i	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
9248.2.a.j	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				544.2.o.d	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-3\beta q^{5}-3q^{9}-4q^{13}+13q^{25}+\cdots\)
9248.2.a.k	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				544.2.o.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-\beta q^{5}-3q^{9}+4q^{13}-3q^{25}-3\beta q^{29}+\cdots\)
9248.2.a.l	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	None	✓				544.2.o.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots\)
9248.2.a.m	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	None	✓				544.2.o.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots\)
9248.2.a.n	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	None	✓				544.2.o.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}-\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
9248.2.a.o	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	None	✓				544.2.o.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
9248.2.a.p	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{2}) \)	None	✓				544.2.a.g	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
9248.2.a.q	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	\(\Q(\sqrt{10}) \)	None	✓				544.2.a.h	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
9248.2.a.r	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9248.2.a.r	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3+\cdots)q^{7}+\cdots\)
9248.2.a.s	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9248.2.a.r	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.t	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	3.3.148.1	None	✓				544.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
9248.2.a.u	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	3.3.148.1	None	✓				544.2.a.i	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9248.2.a.v	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9248.2.a.r	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.w	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9248.2.a.r	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\)
9248.2.a.x	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	✓			9248.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9248.2.a.y	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	✓			9248.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.z	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.45968.1	None	✓	✓			9248.2.a.z	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\cdots)q^{9}+\cdots\)
9248.2.a.ba	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			9248.2.a.ba	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bb	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\zeta_{16})^+\)	\(\Q(\sqrt{-1}) \)	✓				544.2.bb.b	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(\beta _{1}+2\beta _{3})q^{5}-3q^{9}-\beta _{2}q^{13}+(5+\cdots)q^{25}+\cdots\)
9248.2.a.bc	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\zeta_{16})^+\)	\(\Q(\sqrt{-1}) \)	✓				544.2.bb.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(2\beta _{1}+\beta _{3})q^{5}-3q^{9}+5\beta _{2}q^{13}+\cdots\)
9248.2.a.bd	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\zeta_{16})^+\)	None	✓				544.2.b.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots\)
9248.2.a.be	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\zeta_{16})^+\)	None	✓				544.2.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
9248.2.a.bf	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.9248.1	\(\Q(\sqrt{-17}) \)	✓				544.2.b.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(2-\beta _{3})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9248.2.a.bg	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.9248.1	\(\Q(\sqrt{-17}) \)	✓				544.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(4+\beta _{3})q^{9}+\cdots\)
9248.2.a.bh	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			9248.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bi	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.45968.1	None	✓	✓			9248.2.a.z	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bj	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	✓			9248.2.a.x	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.bk	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	✓			9248.2.a.x	$1$	$0$	\(0\)	\(2\)	\(2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.bl	$9248$	$2$	9248.a	1.a	$1$	$6$	$6$	$73.846$	6.6.3359232.1	None	✓				544.2.o.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9248.2.a.bm	$9248$	$2$	9248.a	1.a	$1$	$6$	$6$	$73.846$	6.6.3359232.1	None	✓				544.2.o.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9248.2.a.bn	$9248$	$2$	9248.a	1.a	$1$	$8$	$8$	$73.846$	8.8.3288334336.1	None	✓				544.2.bb.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
9248.2.a.bo	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			9248.2.a.bo	$1$	$1$	\(0\)	\(-9\)	\(-6\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.bp	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			9248.2.a.bo	$1$	$1$	\(0\)	\(-9\)	\(6\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.bq	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			9248.2.a.bo	$1$	$0$	\(0\)	\(9\)	\(-6\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.br	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			9248.2.a.bo	$1$	$0$	\(0\)	\(9\)	\(6\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{5}+\cdots\)
9248.2.a.bs	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9248.2.a.bs	$2$	$1$	\(0\)	\(0\)	\(-12\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots\)
9248.2.a.bt	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9248.2.a.bt	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots\)
9248.2.a.bu	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9248.2.a.bt	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots\)
9248.2.a.bv	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	12.12.\(\cdots\).1	None	✓				544.2.o.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{14}$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{3}-\beta _{4}q^{5}+(-\beta _{6}+\beta _{11})q^{7}+\cdots\)
9248.2.a.bw	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9248.2.a.bs	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{2}-\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots\)
9248.2.a.bx	$9248$	$2$	9248.a	1.a	$1$	$16$	$16$	$73.846$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				544.2.bb.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{12})q^{5}+(\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots\)
9248.2.a.by	$9248$	$2$	9248.a	1.a	$1$	$20$	$20$	$73.846$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		544.2.bb.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{17}q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9248.2.a.bz	$9248$	$2$	9248.a	1.a	$1$	$20$	$20$	$73.846$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		544.2.bb.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{17}q^{3}+\beta _{5}q^{5}-\beta _{12}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9248)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2312))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4624))\)\(^{\oplus 2}\)