Space of modular forms of level 9464, weight 2, and trivial character

• Label: 9464.2.a
• Level: $9464$
• Weight: $2$
• Character orbit: 9464.a
• Rep. character: $\chi_{9464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $232$
• Newform subspaces: $45$
• Sturm bound: $2912$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9464 = 2^{3} \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(2912\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9464))\).

	Total	New	Old
Modular forms	1512	232	1280
Cusp forms	1401	232	1169
Eisenstein series	111	0	111

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

\(2\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(175\)	\(29\)	\(146\)		\(162\)	\(29\)	\(133\)		\(13\)	\(0\)	\(13\)
\(+\)	\(+\)	\(-\)	\(-\)		\(201\)	\(30\)	\(171\)		\(187\)	\(30\)	\(157\)		\(14\)	\(0\)	\(14\)
\(+\)	\(-\)	\(+\)	\(-\)		\(203\)	\(34\)	\(169\)		\(189\)	\(34\)	\(155\)		\(14\)	\(0\)	\(14\)
\(+\)	\(-\)	\(-\)	\(+\)		\(177\)	\(24\)	\(153\)		\(163\)	\(24\)	\(139\)		\(14\)	\(0\)	\(14\)
\(-\)	\(+\)	\(+\)	\(-\)		\(189\)	\(30\)	\(159\)		\(175\)	\(30\)	\(145\)		\(14\)	\(0\)	\(14\)
\(-\)	\(+\)	\(-\)	\(+\)		\(191\)	\(27\)	\(164\)		\(177\)	\(27\)	\(150\)		\(14\)	\(0\)	\(14\)
\(-\)	\(-\)	\(+\)	\(+\)		\(189\)	\(25\)	\(164\)		\(175\)	\(25\)	\(150\)		\(14\)	\(0\)	\(14\)
\(-\)	\(-\)	\(-\)	\(-\)		\(187\)	\(33\)	\(154\)		\(173\)	\(33\)	\(140\)		\(14\)	\(0\)	\(14\)
Plus space			\(+\)		\(732\)	\(105\)	\(627\)		\(677\)	\(105\)	\(572\)		\(55\)	\(0\)	\(55\)
Minus space			\(-\)		\(780\)	\(127\)	\(653\)		\(724\)	\(127\)	\(597\)		\(56\)	\(0\)	\(56\)

Trace form

232 * q + 2 * q^3 + 2 * q^5 + 224 * q^9 - 4 * q^11 - 16 * q^15 - 4 * q^17 + 6 * q^19 + 2 * q^21 - 8 * q^23 + 232 * q^25 - 4 * q^27 - 8 * q^29 - 12 * q^31 - 24 * q^33 + 6 * q^35 + 20 * q^37 - 4 * q^41 + 8 * q^43 - 14 * q^45 + 4 * q^47 + 232 * q^49 + 36 * q^51 - 12 * q^53 + 24 * q^55 - 4 * q^57 + 30 * q^59 + 18 * q^61 - 4 * q^63 + 24 * q^67 - 40 * q^69 + 8 * q^71 - 8 * q^73 - 18 * q^75 - 4 * q^77 + 188 * q^81 - 26 * q^83 - 4 * q^85 + 36 * q^87 - 32 * q^93 + 40 * q^95 - 12 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9464))\) 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	13
9464.2.a.a	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{15}+\cdots\)
9464.2.a.b	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-3q^{11}+4q^{17}+\cdots\)
9464.2.a.c	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				56.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}+4q^{11}-6q^{17}+\cdots\)
9464.2.a.d	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}-2q^{11}+7q^{19}+\cdots\)
9464.2.a.e	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-q^{7}+q^{9}-6q^{15}+\cdots\)
9464.2.a.f	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.s.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-2q^{15}+\cdots\)
9464.2.a.g	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				728.2.s.a	$1$	$1$	\(0\)	\(2\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}+2q^{15}+\cdots\)
9464.2.a.h	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓				56.2.a.b	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
9464.2.a.i	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.bm.a	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9464.2.a.j	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.bm.a	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-\beta q^{5}+q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9464.2.a.k	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{2}) \)	None	✓				728.2.a.e	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
9464.2.a.l	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.s.d	$1$	$2$	\(0\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-2-\beta )q^{5}-q^{7}+\cdots\)
9464.2.a.m	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.s.c	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.n	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.o	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.s.c	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.p	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓				728.2.s.d	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
9464.2.a.q	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{5}) \)	None	✓				728.2.s.b	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
9464.2.a.r	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{17}) \)	None	✓				728.2.a.g	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
9464.2.a.s	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{5}) \)	None	✓				728.2.s.b	$1$	$1$	\(0\)	\(1\)	\(5\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
9464.2.a.t	$9464$	$2$	9464.a	1.a	$1$	$3$	$3$	$75.570$	\(\Q(\zeta_{14})^+\)	None	✓	✓			9464.2.a.t	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\cdots\)
9464.2.a.u	$9464$	$2$	9464.a	1.a	$1$	$3$	$3$	$75.570$	\(\Q(\zeta_{14})^+\)	None	✓	✓			9464.2.a.t	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
9464.2.a.v	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.27004.1	None	✓				728.2.s.f	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3})q^{5}+q^{7}+\cdots\)
9464.2.a.w	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.27004.1	None	✓				728.2.s.f	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}-q^{7}+\cdots\)
9464.2.a.x	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.122260.1	None	✓				728.2.k.a	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{1})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.y	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.122260.1	None	✓				728.2.k.a	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{1})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.z	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.64268.1	None	✓				728.2.a.i	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.ba	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.183064.1	None	✓				728.2.a.h	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
9464.2.a.bb	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.21801.1	None	✓				728.2.s.e	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1})q^{5}+q^{7}+\cdots\)
9464.2.a.bc	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.21801.1	None	✓				728.2.s.e	$1$	$0$	\(0\)	\(3\)	\(5\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)
9464.2.a.bd	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.415174304.1	None	✓				728.2.k.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{5}-q^{7}+\cdots\)
9464.2.a.be	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.415174304.1	None	✓				728.2.k.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4}+\beta _{5})q^{5}+q^{7}+\cdots\)
9464.2.a.bf	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.7674048.1	None	✓				728.2.bm.b	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
9464.2.a.bg	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.7674048.1	None	✓				728.2.bm.b	$1$	$1$	\(0\)	\(2\)	\(4\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bh	$9464$	$2$	9464.a	1.a	$1$	$7$	$7$	$75.570$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				728.2.s.g	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(7\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bi	$9464$	$2$	9464.a	1.a	$1$	$7$	$7$	$75.570$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				728.2.s.g	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-7\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bj	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9464.2.a.bj	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(\beta _{5}+\beta _{6})q^{9}+\cdots\)
9464.2.a.bk	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9464.2.a.bj	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{7}q^{5}-q^{7}+(\beta _{5}+\beta _{6})q^{9}+\cdots\)
9464.2.a.bl	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				728.2.bm.c	$1$	$0$	\(0\)	\(2\)	\(-8\)	\(-12\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{6})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bm	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				728.2.bm.c	$1$	$0$	\(0\)	\(2\)	\(8\)	\(12\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{6})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bn	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9464.2.a.bn	$1$	$1$	\(0\)	\(3\)	\(-8\)	\(-12\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bo	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9464.2.a.bn	$1$	$0$	\(0\)	\(3\)	\(8\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bp	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9464.2.a.bp	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
9464.2.a.bq	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9464.2.a.bp	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-12\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
9464.2.a.br	$9464$	$2$	9464.a	1.a	$1$	$15$	$15$	$75.570$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		9464.2.a.br	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(-15\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9464.2.a.bs	$9464$	$2$	9464.a	1.a	$1$	$15$	$15$	$75.570$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		9464.2.a.br	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(15\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9464)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4732))\)\(^{\oplus 2}\)