Space of modular forms of level 9801, weight 2, and trivial character

• Label: 9801.2.a
• Level: $9801$
• Weight: $2$
• Character orbit: 9801.a
• Rep. character: $\chi_{9801}(1,\cdot)$
• Character field: $\Q$
• Dimension: $418$
• Newform subspaces: $70$
• Sturm bound: $2376$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 9801 = 3^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9801.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 70 \)
Sturm bound:			\(2376\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9801))\).

	Total	New	Old
Modular forms	1260	454	806
Cusp forms	1117	418	699
Eisenstein series	143	36	107

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

\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(306\)	\(106\)	\(200\)		\(271\)	\(98\)	\(173\)		\(35\)	\(8\)	\(27\)
\(+\)	\(-\)	\(-\)		\(324\)	\(120\)	\(204\)		\(288\)	\(110\)	\(178\)		\(36\)	\(10\)	\(26\)
\(-\)	\(+\)	\(-\)		\(324\)	\(118\)	\(206\)		\(288\)	\(110\)	\(178\)		\(36\)	\(8\)	\(28\)
\(-\)	\(-\)	\(+\)		\(306\)	\(110\)	\(196\)		\(270\)	\(100\)	\(170\)		\(36\)	\(10\)	\(26\)
Plus space		\(+\)		\(612\)	\(216\)	\(396\)		\(541\)	\(198\)	\(343\)		\(71\)	\(18\)	\(53\)
Minus space		\(-\)		\(648\)	\(238\)	\(410\)		\(576\)	\(220\)	\(356\)		\(72\)	\(18\)	\(54\)

Trace form

418 * q + 398 * q^4 - 6 * q^10 - 6 * q^13 + 370 * q^16 + 332 * q^25 + 12 * q^28 + 14 * q^34 - 18 * q^37 - 18 * q^40 + 12 * q^43 + 36 * q^46 + 334 * q^49 + 18 * q^52 + 18 * q^58 - 18 * q^61 + 338 * q^64 + 20 * q^67 + 4 * q^70 - 18 * q^73 - 36 * q^76 - 36 * q^82 - 42 * q^85 + 36 * q^94 - 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9801))\) 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	11
9801.2.a.a	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.c	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{5}-4q^{7}-4q^{10}+\cdots\)
9801.2.a.b	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓	✓			9801.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots\)
9801.2.a.c	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-4q^{7}+3q^{8}-q^{10}+\cdots\)
9801.2.a.d	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				891.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
9801.2.a.e	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓	✓			9801.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-2q^{7}+3q^{8}-2q^{10}+\cdots\)
9801.2.a.f	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}+4q^{7}-2q^{13}+4q^{16}+\cdots\)
9801.2.a.g	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}+4q^{7}-2q^{13}+4q^{16}+\cdots\)
9801.2.a.h	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓	✓			9801.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-2q^{7}-3q^{8}-2q^{10}+\cdots\)
9801.2.a.i	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.a	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-4q^{7}-3q^{8}-q^{10}+\cdots\)
9801.2.a.j	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				891.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots\)
9801.2.a.k	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓	✓			9801.2.a.b	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+2q^{7}-3q^{8}+2q^{10}+\cdots\)
9801.2.a.l	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	\(\Q\)	None	✓				99.2.e.c	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}-4q^{7}-4q^{10}+\cdots\)
9801.2.a.m	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{5}) \)	None	✓				99.2.m.a	$1$	$1$	\(-3\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}-2\beta q^{5}+q^{7}+\cdots\)
9801.2.a.n	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{5}) \)	None	✓				99.2.m.a	$1$	$1$	\(-3\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+2\beta q^{5}-q^{7}+\cdots\)
9801.2.a.o	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{13}) \)	None	✓				891.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(1-2\beta )q^{7}+\cdots\)
9801.2.a.p	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓				1089.2.e.f	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-1-\beta )q^{5}+4q^{16}+(2+2\beta )q^{20}+\cdots\)
9801.2.a.q	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓				1089.2.e.f	$2$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(1+\beta )q^{5}+4q^{16}+(-2-2\beta )q^{20}+\cdots\)
9801.2.a.r	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓				1089.2.e.e	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-3q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
9801.2.a.s	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.s	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-3q^{5}-\beta q^{8}-3\beta q^{10}+\cdots\)
9801.2.a.t	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.t	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
9801.2.a.u	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.t	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{5}+(-3+\beta )q^{7}+\cdots\)
9801.2.a.v	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓				81.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{5}-2q^{7}-\beta q^{8}+\cdots\)
9801.2.a.w	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.t	$1$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{5}+(3-\beta )q^{7}-\beta q^{8}+\cdots\)
9801.2.a.x	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.t	$1$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{5}+(3+\beta )q^{7}-\beta q^{8}+\cdots\)
9801.2.a.y	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓	✓			9801.2.a.s	$2$	$1$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+3q^{5}-\beta q^{8}+3\beta q^{10}+\cdots\)
9801.2.a.z	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{3}) \)	None	✓				1089.2.e.e	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
9801.2.a.ba	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{13}) \)	None	✓				891.2.a.i	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(1-2\beta )q^{7}+\cdots\)
9801.2.a.bb	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{5}) \)	None	✓				99.2.m.a	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-2\beta q^{5}-q^{7}+\cdots\)
9801.2.a.bc	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	\(\Q(\sqrt{5}) \)	None	✓				99.2.m.a	$1$	$0$	\(3\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+2\beta q^{5}+q^{7}+\cdots\)
9801.2.a.bd	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	\(\Q(\zeta_{18})^+\)	None	✓				99.2.e.d	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
9801.2.a.be	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	\(\Q(\zeta_{18})^+\)	None	✓				99.2.e.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.bf	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	3.3.837.1	None	✓				891.2.a.m	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
9801.2.a.bg	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	3.3.837.1	None	✓				891.2.a.m	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
9801.2.a.bh	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.4752.1	None	✓				891.2.a.o	$1$	$1$	\(-2\)	\(0\)	\(8\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
9801.2.a.bi	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.22545.1	None	✓				99.2.e.e	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
9801.2.a.bj	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.8112.1	None	✓	✓			9801.2.a.bj	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\cdots\)
9801.2.a.bk	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.8112.1	None	✓	✓			9801.2.a.bj	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
9801.2.a.bl	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.22545.1	None	✓				99.2.e.e	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
9801.2.a.bm	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.4752.1	None	✓				891.2.a.o	$1$	$1$	\(2\)	\(0\)	\(-8\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
9801.2.a.bn	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
9801.2.a.bo	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
9801.2.a.bp	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
9801.2.a.bq	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	\(1\)	\(0\)	\(4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
9801.2.a.br	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.19783872.1	None	✓	✓			9801.2.a.br	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.bs	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.19783872.1	None	✓	✓			9801.2.a.br	$2$	$1$	\(0\)	\(0\)	\(8\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.bt	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.191244096.1	None	✓				1089.2.e.j	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
9801.2.a.bu	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.191244096.1	None	✓				1089.2.e.j	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{4})q^{4}+\beta _{3}q^{5}+\cdots\)
9801.2.a.bv	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓	✓			9801.2.a.bv	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\beta _{4}q^{7}+\cdots\)
9801.2.a.bw	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓	✓			9801.2.a.bv	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{4}q^{7}+\cdots\)
9801.2.a.bx	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓	✓			9801.2.a.bx	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+(1-\beta _{2}-\beta _{6}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
9801.2.a.by	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓	✓			9801.2.a.bx	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{2}+(1-\beta _{2}-\beta _{6}-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
9801.2.a.bz	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓				1089.2.e.k	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}+\beta _{6})q^{2}+(2+\beta _{3})q^{4}-\beta _{4}q^{5}+\cdots\)
9801.2.a.ca	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.\(\cdots\).1	None	✓				1089.2.e.k	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}+\beta _{6})q^{2}+(2+\beta _{3})q^{4}+\beta _{4}q^{5}+\cdots\)
9801.2.a.cb	$9801$	$2$	9801.a	1.a	$1$	$10$	$10$	$78.261$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1089.2.e.l	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.cc	$9801$	$2$	9801.a	1.a	$1$	$10$	$10$	$78.261$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1089.2.e.l	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.cd	$9801$	$2$	9801.a	1.a	$1$	$10$	$10$	$78.261$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1089.2.e.l	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.ce	$9801$	$2$	9801.a	1.a	$1$	$10$	$10$	$78.261$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1089.2.e.l	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
9801.2.a.cf	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				891.2.f.c	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(1+\cdots)q^{7}+\cdots\)
9801.2.a.cg	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				891.2.f.c	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots\)
9801.2.a.ch	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				1089.2.e.n	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{7}q^{2}-\beta _{5}q^{4}+(-1-\beta _{1})q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
9801.2.a.ci	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				1089.2.e.n	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{7}q^{2}-\beta _{5}q^{4}+(1+\beta _{1})q^{5}+(\beta _{7}+\cdots)q^{7}+\cdots\)
9801.2.a.cj	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9801.2.a.cj	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{7}q^{2}+(1-\beta _{2})q^{4}+(-\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
9801.2.a.ck	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				891.2.f.c	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots\)
9801.2.a.cl	$9801$	$2$	9801.a	1.a	$1$	$12$	$12$	$78.261$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				891.2.f.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(1+\cdots)q^{7}+\cdots\)
9801.2.a.cm	$9801$	$2$	9801.a	1.a	$1$	$18$	$18$	$78.261$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		99.2.m.b	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
9801.2.a.cn	$9801$	$2$	9801.a	1.a	$1$	$18$	$18$	$78.261$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				99.2.m.b	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
9801.2.a.co	$9801$	$2$	9801.a	1.a	$1$	$18$	$18$	$78.261$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		99.2.m.b	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
9801.2.a.cp	$9801$	$2$	9801.a	1.a	$1$	$18$	$18$	$78.261$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				99.2.m.b	$1$	$0$	\(2\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
9801.2.a.cq	$9801$	$2$	9801.a	1.a	$1$	$24$	$24$	$78.261$		None	✓		✓		891.2.f.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-18\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
9801.2.a.cr	$9801$	$2$	9801.a	1.a	$1$	$24$	$24$	$78.261$		None	✓		✓		891.2.f.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(18\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9801)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3267))\)\(^{\oplus 2}\)