Space of modular forms of level 8649, weight 2, and trivial character

• Label: 8649.2.a
• Level: $8649$
• Weight: $2$
• Character orbit: 8649.a
• Rep. character: $\chi_{8649}(1,\cdot)$
• Character field: $\Q$
• Dimension: $372$
• Newform subspaces: $49$
• Sturm bound: $1984$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 8649 = 3^{2} \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8649.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(1984\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8649))\).

	Total	New	Old
Modular forms	1056	401	655
Cusp forms	929	372	557
Eisenstein series	127	29	98

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

\(3\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(69\)
\(+\)	\(-\)	\(-\)	\(85\)
\(-\)	\(+\)	\(-\)	\(113\)
\(-\)	\(-\)	\(+\)	\(105\)
Plus space		\(+\)	\(174\)
Minus space		\(-\)	\(198\)

Trace form

372 * q - 2 * q^2 + 354 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 4 * q^10 - 4 * q^11 + 12 * q^14 + 326 * q^16 - 12 * q^19 + 2 * q^20 + 10 * q^22 - 6 * q^23 + 304 * q^25 - 4 * q^26 + 4 * q^28 + 4 * q^29 + 16 * q^32 + 24 * q^34 + 10 * q^35 - 6 * q^37 + 32 * q^38 + 48 * q^40 + 6 * q^43 - 6 * q^44 - 6 * q^46 + 18 * q^47 + 264 * q^49 + 28 * q^50 + 62 * q^52 - 22 * q^53 + 36 * q^55 + 24 * q^56 + 50 * q^58 + 16 * q^59 - 12 * q^61 + 310 * q^64 - 26 * q^65 + 26 * q^67 + 30 * q^68 + 100 * q^70 + 4 * q^71 - 30 * q^73 - 4 * q^74 - 8 * q^76 - 4 * q^77 - 14 * q^79 + 18 * q^80 + 6 * q^82 - 16 * q^83 - 34 * q^85 - 28 * q^86 + 20 * q^88 - 12 * q^89 + 6 * q^91 + 36 * q^92 - 26 * q^94 + 18 * q^95 - 36 * q^97 - 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8649))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	31
8649.2.a.a	$8649$	$2$	8649.a	1.a	$1$	$1$	$1$	$69.063$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				279.2.h.a	$2$	$2$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-4q^{7}-5q^{13}+4q^{16}-7q^{19}+\cdots\)
8649.2.a.b	$8649$	$2$	8649.a	1.a	$1$	$1$	$1$	$69.063$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				279.2.h.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-4q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
8649.2.a.c	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				31.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-3+2\beta )q^{7}+\cdots\)
8649.2.a.d	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				2883.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(1-2\beta )q^{7}+\cdots\)
8649.2.a.e	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				2883.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(1-2\beta )q^{7}+\cdots\)
8649.2.a.f	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				31.2.d.a	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
8649.2.a.g	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				31.2.d.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
8649.2.a.h	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{2}) \)	None	✓				93.2.e.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{5}+(-2-2\beta )q^{7}+\cdots\)
8649.2.a.i	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{2}) \)	None	✓				93.2.e.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{5}+(-2-2\beta )q^{7}+\cdots\)
8649.2.a.j	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{2}) \)	None	✓				961.2.a.b	$2$	$1$	\(2\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{7}-3q^{8}+2\beta q^{11}+\cdots\)
8649.2.a.k	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{2}) \)	None	✓				31.2.c.a	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(1+\beta )q^{7}+\cdots\)
8649.2.a.l	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{2}) \)	None	✓				31.2.c.a	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(1+\beta )q^{7}+\cdots\)
8649.2.a.m	$8649$	$2$	8649.a	1.a	$1$	$2$	$2$	$69.063$	\(\Q(\sqrt{5}) \)	None	✓				93.2.a.a	$1$	$1$	\(3\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(3-2\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
8649.2.a.n	$8649$	$2$	8649.a	1.a	$1$	$3$	$3$	$69.063$	3.3.148.1	None	✓				93.2.e.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.o	$8649$	$2$	8649.a	1.a	$1$	$3$	$3$	$69.063$	3.3.148.1	None	✓				93.2.e.b	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.p	$8649$	$2$	8649.a	1.a	$1$	$3$	$3$	$69.063$	3.3.229.1	None	✓				93.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8649.2.a.q	$8649$	$2$	8649.a	1.a	$1$	$3$	$3$	$69.063$	3.3.837.1	\(\Q(\sqrt{-31}) \)	✓				961.2.a.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
8649.2.a.r	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				961.2.a.h	$2$	$1$	\(-6\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+3\beta _{2}q^{4}+(1-2\beta _{2}+\cdots)q^{5}+\cdots\)
8649.2.a.s	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\zeta_{15})^+\)	\(\Q(\sqrt{-3}) \)	✓				279.2.y.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-2\beta _{2}-3\beta _{3})q^{7}+(-1-3\beta _{1}+\cdots)q^{13}+\cdots\)
8649.2.a.t	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\zeta_{15})^+\)	\(\Q(\sqrt{-3}) \)	✓				279.2.y.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-2\beta _{2}-3\beta _{3})q^{7}+(1+3\beta _{1}+\cdots)q^{13}+\cdots\)
8649.2.a.u	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				279.2.h.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
8649.2.a.v	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				279.2.h.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
8649.2.a.w	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\zeta_{15})^+\)	None	✓				93.2.f.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
8649.2.a.x	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	\(\Q(\zeta_{15})^+\)	None	✓				93.2.f.a	$1$	$1$	\(1\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
8649.2.a.y	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	4.4.8768.1	None	✓				2883.2.a.i	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.z	$8649$	$2$	8649.a	1.a	$1$	$4$	$4$	$69.063$	4.4.8768.1	None	✓				2883.2.a.i	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.ba	$8649$	$2$	8649.a	1.a	$1$	$6$	$6$	$69.063$	6.6.1389928896.1	\(\Q(\sqrt{-31}) \)	✓	✓			8649.2.a.ba	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
8649.2.a.bb	$8649$	$2$	8649.a	1.a	$1$	$6$	$6$	$69.063$	6.6.361944768.1	None	✓				279.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}-\beta _{2}q^{5}+(1+\beta _{5})q^{7}+\cdots\)
8649.2.a.bc	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.1413480448.1	None	✓				2883.2.a.q	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{7})q^{2}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
8649.2.a.bd	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.1413480448.1	None	✓				2883.2.a.q	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{7})q^{2}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
8649.2.a.be	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.2051578125.1	None	✓				31.2.g.a	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots\)
8649.2.a.bf	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.2051578125.1	None	✓				31.2.g.a	$1$	$0$	\(-2\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots\)
8649.2.a.bg	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				93.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
8649.2.a.bh	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				93.2.f.b	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
8649.2.a.bi	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.1697203125.1	None	✓				93.2.m.a	$1$	$1$	\(5\)	\(0\)	\(6\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
8649.2.a.bj	$8649$	$2$	8649.a	1.a	$1$	$8$	$8$	$69.063$	8.8.1697203125.1	None	✓				93.2.m.a	$1$	$0$	\(5\)	\(0\)	\(6\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
8649.2.a.bk	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				93.2.m.b	$1$	$0$	\(-5\)	\(0\)	\(-6\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.bl	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				93.2.m.b	$1$	$1$	\(-5\)	\(0\)	\(-6\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
8649.2.a.bm	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8649.2.a.bm	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{7})q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
8649.2.a.bn	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				279.2.i.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots\)
8649.2.a.bo	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				279.2.i.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots\)
8649.2.a.bp	$8649$	$2$	8649.a	1.a	$1$	$12$	$12$	$69.063$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				961.2.a.k	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{8}q^{2}+(1+\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
8649.2.a.bq	$8649$	$2$	8649.a	1.a	$1$	$16$	$16$	$69.063$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				279.2.y.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
8649.2.a.br	$8649$	$2$	8649.a	1.a	$1$	$16$	$16$	$69.063$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				279.2.y.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
8649.2.a.bs	$8649$	$2$	8649.a	1.a	$1$	$16$	$16$	$69.063$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				961.2.a.l	$2$	$0$	\(8\)	\(0\)	\(16\)	\(-16\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{8}-\beta _{13})q^{2}+(-\beta _{4}+\beta _{15})q^{4}+\cdots\)
8649.2.a.bt	$8649$	$2$	8649.a	1.a	$1$	$24$	$24$	$69.063$		None	✓	✓	✓		8649.2.a.bt	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8649.2.a.bu	$8649$	$2$	8649.a	1.a	$1$	$24$	$24$	$69.063$		None	✓				2883.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8649.2.a.bv	$8649$	$2$	8649.a	1.a	$1$	$24$	$24$	$69.063$		None	✓				2883.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8649.2.a.bw	$8649$	$2$	8649.a	1.a	$1$	$32$	$32$	$69.063$		None	✓	✓	✓		8649.2.a.bw	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-32\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8649))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8649)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(961))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2883))\)\(^{\oplus 2}\)