Space of modular forms of level 8464, weight 2, and trivial character

• Label: 8464.2.a
• Level: $8464$
• Weight: $2$
• Character orbit: 8464.a
• Rep. character: $\chi_{8464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $242$
• Newform subspaces: $62$
• Sturm bound: $2208$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 8464 = 2^{4} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 62 \)
Sturm bound:			\(2208\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8464))\).

	Total	New	Old
Modular forms	1176	263	913
Cusp forms	1033	242	791
Eisenstein series	143	21	122

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

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(288\)	\(60\)	\(228\)		\(253\)	\(60\)	\(193\)		\(35\)	\(0\)	\(35\)
\(+\)	\(-\)	\(-\)		\(300\)	\(66\)	\(234\)		\(264\)	\(66\)	\(198\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(-\)		\(300\)	\(71\)	\(229\)		\(264\)	\(61\)	\(203\)		\(36\)	\(10\)	\(26\)
\(-\)	\(-\)	\(+\)		\(288\)	\(66\)	\(222\)		\(252\)	\(55\)	\(197\)		\(36\)	\(11\)	\(25\)
Plus space		\(+\)		\(576\)	\(126\)	\(450\)		\(505\)	\(115\)	\(390\)		\(71\)	\(11\)	\(60\)
Minus space		\(-\)		\(600\)	\(137\)	\(463\)		\(528\)	\(127\)	\(401\)		\(72\)	\(10\)	\(62\)

Trace form

242 * q - 2 * q^3 + 2 * q^5 - 4 * q^7 + 224 * q^9 + 2 * q^13 + 2 * q^17 - 4 * q^19 + 204 * q^25 - 8 * q^27 + 2 * q^29 - 10 * q^31 + 8 * q^33 + 10 * q^37 - 20 * q^39 - 6 * q^41 + 10 * q^45 + 44 * q^47 + 176 * q^49 - 4 * q^51 + 10 * q^53 + 24 * q^55 - 8 * q^57 - 2 * q^59 + 18 * q^61 - 32 * q^63 - 12 * q^65 + 8 * q^67 + 6 * q^71 + 2 * q^73 - 6 * q^75 + 8 * q^77 - 28 * q^79 + 162 * q^81 + 20 * q^83 + 12 * q^85 + 40 * q^87 - 6 * q^89 - 4 * q^91 - 22 * q^93 - 8 * q^95 - 6 * q^97 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8464))\) 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	23
8464.2.a.a	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				1058.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}-2q^{7}+6q^{9}+4q^{11}+\cdots\)
8464.2.a.b	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				184.2.a.d	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+6q^{9}-5q^{13}+6q^{17}+\cdots\)
8464.2.a.c	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				1058.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+2q^{7}+6q^{9}-4q^{11}+\cdots\)
8464.2.a.d	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.h	$1$	$2$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
8464.2.a.e	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.h	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
8464.2.a.f	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots\)
8464.2.a.g	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				46.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
8464.2.a.h	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
8464.2.a.i	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}-6q^{17}+\cdots\)
8464.2.a.j	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
8464.2.a.k	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
8464.2.a.l	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+2q^{7}-2q^{9}-6q^{11}+\cdots\)
8464.2.a.m	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				184.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\)
8464.2.a.n	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}-2q^{9}+6q^{11}+\cdots\)
8464.2.a.o	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				4232.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
8464.2.a.p	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				184.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
8464.2.a.q	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				1058.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
8464.2.a.r	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				1058.2.a.a	$1$	$1$	\(0\)	\(2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
8464.2.a.s	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	\(\Q\)	None	✓				92.2.a.a	$1$	$1$	\(0\)	\(3\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
8464.2.a.t	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{2}) \)	None	✓				1058.2.a.h	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2\beta q^{7}+q^{9}+3\beta q^{11}+6q^{13}+\cdots\)
8464.2.a.u	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				529.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
8464.2.a.v	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				2116.2.a.f	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+\beta q^{7}-2q^{9}+\beta q^{11}+\cdots\)
8464.2.a.w	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				1058.2.a.f	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2\beta q^{5}-2\beta q^{7}-2q^{9}+2\beta q^{11}+\cdots\)
8464.2.a.x	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				529.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
8464.2.a.y	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{6}) \)	None	✓				4232.2.a.p	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-3q^{5}+(-2-\beta )q^{7}+3q^{9}+\cdots\)
8464.2.a.z	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{2}) \)	None	✓				529.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-2\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
8464.2.a.ba	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{2}) \)	None	✓				529.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+2\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
8464.2.a.bb	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
8464.2.a.bc	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{6}) \)	None	✓				4232.2.a.p	$1$	$0$	\(0\)	\(0\)	\(6\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+3q^{5}+(2+\beta )q^{7}+3q^{9}+\beta q^{11}+\cdots\)
8464.2.a.bd	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{17}) \)	None	✓				184.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
8464.2.a.be	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				4232.2.a.m	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
8464.2.a.bf	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				4232.2.a.m	$1$	$0$	\(0\)	\(2\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
8464.2.a.bg	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{2}) \)	None	✓				4232.2.a.k	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}-q^{5}-3\beta q^{7}+(3+4\beta )q^{9}+\cdots\)
8464.2.a.bh	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				1058.2.a.g	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
8464.2.a.bi	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{3}) \)	None	✓				2116.2.a.e	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+q^{13}+\cdots\)
8464.2.a.bj	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	\(\Q(\sqrt{2}) \)	None	✓				4232.2.a.k	$1$	$0$	\(0\)	\(4\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}+q^{5}+3\beta q^{7}+(3+4\beta )q^{9}+\cdots\)
8464.2.a.bk	$8464$	$2$	8464.a	1.a	$1$	$3$	$3$	$67.585$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓				529.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+\beta _{2}q^{3}+(3-\beta _{1}-\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)
8464.2.a.bl	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\zeta_{24})^+\)	None	✓				4232.2.a.s	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-2-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
8464.2.a.bm	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				4232.2.a.t	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+2q^{9}+\cdots\)
8464.2.a.bn	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\zeta_{24})^+\)	None	✓				4232.2.a.s	$1$	$1$	\(0\)	\(0\)	\(8\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
8464.2.a.bo	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	4.4.9248.1	None	✓				4232.2.a.r	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
8464.2.a.bp	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\sqrt{2}, \sqrt{13})\)	None	✓				529.2.a.h	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}-2q^{9}+\cdots\)
8464.2.a.bq	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\zeta_{24})^+\)	None	✓				1058.2.a.i	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(\beta _{1}+2\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.br	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	\(\Q(\zeta_{24})^+\)	None	✓				529.2.a.g	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
8464.2.a.bs	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				23.2.c.a	$1$	$0$	\(0\)	\(-2\)	\(-7\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8464.2.a.bt	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				23.2.c.a	$1$	$1$	\(0\)	\(-2\)	\(7\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
8464.2.a.bu	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
8464.2.a.bv	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{5}+\cdots\)
8464.2.a.bw	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.a	$1$	$1$	\(0\)	\(2\)	\(-8\)	\(7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{3}+(-2+\beta _{1}+\beta _{3})q^{5}+\cdots\)
8464.2.a.bx	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.a	$1$	$0$	\(0\)	\(2\)	\(8\)	\(-7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{3}+(2-\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8464.2.a.by	$8464$	$2$	8464.a	1.a	$1$	$6$	$6$	$67.585$	6.6.26849792.2	None	✓				4232.2.a.v	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-\beta _{3}+\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)
8464.2.a.bz	$8464$	$2$	8464.a	1.a	$1$	$6$	$6$	$67.585$	6.6.197448192.1	None	✓				2116.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(3+\cdots)q^{9}+\cdots\)
8464.2.a.ca	$8464$	$2$	8464.a	1.a	$1$	$8$	$8$	$67.585$	8.8.5780865024.1	None	✓				2116.2.a.h	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{5})q^{3}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
8464.2.a.cb	$8464$	$2$	8464.a	1.a	$1$	$8$	$8$	$67.585$	8.8.\(\cdots\).1	None	✓				1058.2.a.n	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{4})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8464.2.a.cc	$8464$	$2$	8464.a	1.a	$1$	$8$	$8$	$67.585$	8.8.\(\cdots\).1	None	✓				4232.2.a.w	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{5})q^{7}+(2+\cdots)q^{9}+\cdots\)
8464.2.a.cd	$8464$	$2$	8464.a	1.a	$1$	$10$	$10$	$67.585$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		92.2.e.a	$1$	$1$	\(0\)	\(-1\)	\(-12\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots\)
8464.2.a.ce	$8464$	$2$	8464.a	1.a	$1$	$10$	$10$	$67.585$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		92.2.e.a	$1$	$0$	\(0\)	\(-1\)	\(12\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
8464.2.a.cf	$8464$	$2$	8464.a	1.a	$1$	$12$	$12$	$67.585$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				4232.2.a.x	$2$	$1$	\(0\)	\(-8\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{9}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8464.2.a.cg	$8464$	$2$	8464.a	1.a	$1$	$15$	$15$	$67.585$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				184.2.i.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5}+\beta _{10})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.ch	$8464$	$2$	8464.a	1.a	$1$	$15$	$15$	$67.585$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				184.2.i.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}-\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.ci	$8464$	$2$	8464.a	1.a	$1$	$15$	$15$	$67.585$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				184.2.i.a	$1$	$1$	\(0\)	\(1\)	\(-10\)	\(10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{13})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.cj	$8464$	$2$	8464.a	1.a	$1$	$15$	$15$	$67.585$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				184.2.i.a	$1$	$0$	\(0\)	\(1\)	\(10\)	\(-10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{13})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8464)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4232))\)\(^{\oplus 2}\)