Space of modular forms of level 8281, weight 2, and trivial character

• Label: 8281.2.a
• Level: $8281$
• Weight: $2$
• Character orbit: 8281.a
• Rep. character: $\chi_{8281}(1,\cdot)$
• Character field: $\Q$
• Dimension: $502$
• Newform subspaces: $78$
• Sturm bound: $1698$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 78 \)
Sturm bound:			\(1698\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8281))\).

	Total	New	Old
Modular forms	904	557	347
Cusp forms	793	502	291
Eisenstein series	111	55	56

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

\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(219\)	\(128\)	\(91\)		\(192\)	\(118\)	\(74\)		\(27\)	\(10\)	\(17\)
\(+\)	\(-\)	\(-\)		\(231\)	\(142\)	\(89\)		\(203\)	\(130\)	\(73\)		\(28\)	\(12\)	\(16\)
\(-\)	\(+\)	\(-\)		\(233\)	\(146\)	\(87\)		\(205\)	\(131\)	\(74\)		\(28\)	\(15\)	\(13\)
\(-\)	\(-\)	\(+\)		\(221\)	\(141\)	\(80\)		\(193\)	\(123\)	\(70\)		\(28\)	\(18\)	\(10\)
Plus space		\(+\)		\(440\)	\(269\)	\(171\)		\(385\)	\(241\)	\(144\)		\(55\)	\(28\)	\(27\)
Minus space		\(-\)		\(464\)	\(288\)	\(176\)		\(408\)	\(261\)	\(147\)		\(56\)	\(27\)	\(29\)

Trace form

502 * q - 4 * q^3 + 472 * q^4 + 2 * q^5 + 12 * q^8 + 442 * q^9 + 6 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^15 + 416 * q^16 + 4 * q^18 - 12 * q^19 - 2 * q^20 + 14 * q^22 + 6 * q^23 - 4 * q^24 + 404 * q^25 + 2 * q^27 + 20 * q^29 + 58 * q^30 - 4 * q^31 + 44 * q^32 - 4 * q^33 + 2 * q^34 + 354 * q^36 + 16 * q^37 - 20 * q^38 + 14 * q^40 + 2 * q^41 + 22 * q^43 + 28 * q^44 + 22 * q^45 + 8 * q^46 + 8 * q^47 + 46 * q^48 + 40 * q^50 + 6 * q^51 + 16 * q^53 + 48 * q^54 + 16 * q^55 + 16 * q^57 + 40 * q^58 + 16 * q^59 - 24 * q^61 - 10 * q^62 + 318 * q^64 + 26 * q^66 + 90 * q^68 - 16 * q^69 - 28 * q^71 + 40 * q^72 - 22 * q^73 + 70 * q^74 - 54 * q^75 + 16 * q^76 + 34 * q^79 - 38 * q^80 + 246 * q^81 + 52 * q^82 + 24 * q^83 + 24 * q^85 - 52 * q^86 + 16 * q^87 + 42 * q^88 + 26 * q^89 + 28 * q^90 - 140 * q^92 + 28 * q^93 - 2 * q^94 + 22 * q^95 - 4 * q^96 - 6 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8281))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	13
8281.2.a.a	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				637.2.c.a	$1$	$1$	\(-2\)	\(-2\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.b	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				637.2.c.a	$1$	$1$	\(-2\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.c	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.g.a	$1$	$1$	\(-1\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots\)
8281.2.a.d	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓				49.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
8281.2.a.e	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.f	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.e.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.g	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.g.a	$1$	$0$	\(-1\)	\(3\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots\)
8281.2.a.h	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots\)
8281.2.a.i	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.g.a	$1$	$1$	\(1\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots\)
8281.2.a.j	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.g.a	$1$	$0$	\(1\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots\)
8281.2.a.k	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				637.2.c.a	$1$	$1$	\(2\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.l	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				91.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots\)
8281.2.a.m	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	\(\Q\)	None	✓				637.2.c.a	$1$	$1$	\(2\)	\(2\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.n	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{5}) \)	None	✓				91.2.f.a	$1$	$0$	\(-3\)	\(3\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.o	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{2}) \)	None	✓				637.2.f.e	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.p	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{2}) \)	None	✓				637.2.f.e	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.q	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{3}) \)	None	✓				13.2.e.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8281.2.a.r	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{3}) \)	None	✓				91.2.f.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.s	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{3}) \)	None	✓				91.2.k.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.t	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{3}) \)	None	✓				91.2.f.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.u	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{13}) \)	\(\Q(\sqrt{-91}) \)	✓				637.2.c.b	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots\)
8281.2.a.v	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{2}) \)	None	✓				91.2.a.c	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
8281.2.a.w	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{3}) \)	None	✓				91.2.k.a	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.x	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{2}) \)	None	✓				637.2.f.e	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.y	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{2}) \)	None	✓				637.2.f.e	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.z	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{5}) \)	None	✓				91.2.e.b	$1$	$1$	\(3\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.ba	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{5}) \)	None	✓				91.2.e.b	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.bb	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	\(\Q(\sqrt{5}) \)	None	✓				91.2.f.a	$1$	$0$	\(3\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.bc	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	\(\Q(\sqrt{-7}) \)	✓	✓			8281.2.a.bc	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bd	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	\(\Q(\sqrt{-7}) \)	✓	✓			8281.2.a.bd	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
8281.2.a.be	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓				91.2.c.a	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bf	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	None	✓				169.2.a.b	$1$	$0$	\(-2\)	\(2\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bg	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.316.1	None	✓				91.2.a.d	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.bh	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓				637.2.a.h	$1$	$0$	\(2\)	\(-4\)	\(5\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bi	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓				91.2.c.a	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bj	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	None	✓				169.2.a.b	$1$	$1$	\(2\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bk	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓				637.2.a.h	$1$	$0$	\(2\)	\(4\)	\(-5\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bl	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	\(\Q(\sqrt{-7}) \)	✓	✓			8281.2.a.bd	$2$	$1$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots\)
8281.2.a.bm	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	\(\Q(\zeta_{14})^+\)	\(\Q(\sqrt{-7}) \)	✓	✓			8281.2.a.bc	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots\)
8281.2.a.bn	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	\(\Q(\sqrt{2}, \sqrt{23})\)	None	✓				637.2.f.g	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
8281.2.a.bo	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓				637.2.f.h	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
8281.2.a.bp	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓				91.2.f.c	$1$	$0$	\(-1\)	\(-1\)	\(7\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bq	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				637.2.q.e	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
8281.2.a.br	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	\(\Q(\sqrt{3}, \sqrt{13})\)	None	✓				637.2.q.d	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots\)
8281.2.a.bs	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				637.2.q.e	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
8281.2.a.bt	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓				91.2.f.c	$1$	$0$	\(1\)	\(-1\)	\(-7\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bu	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓				637.2.f.h	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
8281.2.a.bv	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	\(\Q(\sqrt{2}, \sqrt{23})\)	None	✓				637.2.f.g	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8281.2.a.bw	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓				91.2.e.c	$1$	$1$	\(-4\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.bx	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓				91.2.e.c	$1$	$0$	\(-4\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.by	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓				91.2.q.a	$1$	$1$	\(-4\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.bz	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓				91.2.g.b	$1$	$1$	\(-2\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.ca	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓				91.2.g.b	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cb	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.1279733.1	None	✓				1183.2.a.n	$1$	$1$	\(-2\)	\(4\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2}+\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots\)
8281.2.a.cc	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓				637.2.a.m	$1$	$1$	\(0\)	\(-8\)	\(6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.cd	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓				637.2.a.m	$1$	$1$	\(0\)	\(8\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.ce	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓				91.2.g.b	$1$	$1$	\(2\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cf	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓				91.2.g.b	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cg	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.1279733.1	None	✓				1183.2.a.n	$1$	$0$	\(2\)	\(4\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.ch	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓				91.2.q.a	$1$	$1$	\(4\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.ci	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓				637.2.f.l	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
8281.2.a.cj	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				91.2.r.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.ck	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				91.2.r.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.cl	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓				637.2.f.l	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.cm	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8281.2.a.cm	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cn	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				1183.2.a.q	$1$	$1$	\(-3\)	\(-8\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.co	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				91.2.k.b	$2$	$1$	\(0\)	\(-6\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cp	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				91.2.k.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cq	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				1183.2.a.q	$1$	$0$	\(3\)	\(-8\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.cr	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8281.2.a.cm	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cs	$8281$	$2$	8281.a	1.a	$1$	$16$	$16$	$66.124$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				637.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{7}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
8281.2.a.ct	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓		✓		1183.2.e.k	$1$	$1$	\(-1\)	\(0\)	\(-13\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8281.2.a.cu	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓				1183.2.e.k	$1$	$0$	\(-1\)	\(0\)	\(13\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8281.2.a.cv	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓				1183.2.e.k	$1$	$1$	\(1\)	\(0\)	\(-13\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8281.2.a.cw	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓		✓		1183.2.e.k	$1$	$0$	\(1\)	\(0\)	\(13\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8281.2.a.cx	$8281$	$2$	8281.a	1.a	$1$	$32$	$32$	$66.124$		None	✓				637.2.q.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8281.2.a.cy	$8281$	$2$	8281.a	1.a	$1$	$36$	$36$	$66.124$		None	✓	✓	✓		8281.2.a.cy	$2$	$1$	\(-14\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8281.2.a.cz	$8281$	$2$	8281.a	1.a	$1$	$36$	$36$	$66.124$		None	✓	✓	✓		8281.2.a.cy	$2$	$0$	\(14\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8281))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8281)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)