Space of modular forms of level 17298, weight 2, and trivial character

• Label: 17298.2.a
• Level: $17298$
• Weight: $2$
• Character orbit: 17298.a
• Rep. character: $\chi_{17298}(1,\cdot)$
• Character field: $\Q$
• Dimension: $388$
• Newform subspaces: $96$
• Sturm bound: $5952$

Defining parameters

Level:	\( N \)	\(=\)	\( 17298 = 2 \cdot 3^{2} \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	17298.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 96 \)
Sturm bound:			\(5952\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(17298))\).

	Total	New	Old
Modular forms	3104	388	2716
Cusp forms	2849	388	2461
Eisenstein series	255	0	255

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

\(2\)	\(3\)	\(31\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(376\)	\(43\)	\(333\)		\(345\)	\(43\)	\(302\)		\(31\)	\(0\)	\(31\)
\(+\)	\(+\)	\(-\)	\(-\)		\(400\)	\(35\)	\(365\)		\(368\)	\(35\)	\(333\)		\(32\)	\(0\)	\(32\)
\(+\)	\(-\)	\(+\)	\(-\)		\(392\)	\(60\)	\(332\)		\(360\)	\(60\)	\(300\)		\(32\)	\(0\)	\(32\)
\(+\)	\(-\)	\(-\)	\(+\)		\(384\)	\(56\)	\(328\)		\(352\)	\(56\)	\(296\)		\(32\)	\(0\)	\(32\)
\(-\)	\(+\)	\(+\)	\(-\)		\(392\)	\(43\)	\(349\)		\(360\)	\(43\)	\(317\)		\(32\)	\(0\)	\(32\)
\(-\)	\(+\)	\(-\)	\(+\)		\(384\)	\(35\)	\(349\)		\(352\)	\(35\)	\(317\)		\(32\)	\(0\)	\(32\)
\(-\)	\(-\)	\(+\)	\(+\)		\(392\)	\(52\)	\(340\)		\(360\)	\(52\)	\(308\)		\(32\)	\(0\)	\(32\)
\(-\)	\(-\)	\(-\)	\(-\)		\(384\)	\(64\)	\(320\)		\(352\)	\(64\)	\(288\)		\(32\)	\(0\)	\(32\)
Plus space			\(+\)		\(1536\)	\(186\)	\(1350\)		\(1409\)	\(186\)	\(1223\)		\(127\)	\(0\)	\(127\)
Minus space			\(-\)		\(1568\)	\(202\)	\(1366\)		\(1440\)	\(202\)	\(1238\)		\(128\)	\(0\)	\(128\)

Trace form

388 * q + 388 * q^4 + 4 * q^5 + 4 * q^7 + 4 * q^10 - 2 * q^11 - 6 * q^13 - 4 * q^14 + 388 * q^16 - 4 * q^17 + 8 * q^19 + 4 * q^20 + 6 * q^22 + 388 * q^25 + 10 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^34 - 24 * q^35 - 2 * q^37 - 8 * q^38 + 4 * q^40 + 6 * q^43 - 2 * q^44 + 16 * q^46 - 4 * q^47 + 396 * q^49 - 16 * q^50 - 6 * q^52 + 14 * q^53 - 28 * q^55 - 4 * q^56 + 2 * q^58 - 4 * q^59 + 2 * q^61 + 388 * q^64 + 20 * q^65 - 32 * q^67 - 4 * q^68 - 16 * q^70 + 16 * q^71 + 16 * q^73 + 14 * q^74 + 8 * q^76 - 28 * q^77 + 20 * q^79 + 4 * q^80 - 8 * q^82 + 42 * q^83 + 16 * q^85 - 2 * q^86 + 6 * q^88 + 32 * q^89 + 36 * q^91 + 16 * q^95 + 20 * q^97 + 32 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(17298))\) 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	3	31
17298.2.a.a	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
17298.2.a.b	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
17298.2.a.c	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
17298.2.a.d	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+3q^{11}+\cdots\)
17298.2.a.e	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
17298.2.a.f	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
17298.2.a.g	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-2q^{13}+\cdots\)
17298.2.a.h	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
17298.2.a.i	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
17298.2.a.j	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots\)
17298.2.a.k	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-4q^{7}+q^{8}-3q^{10}+\cdots\)
17298.2.a.l	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-2q^{7}+q^{8}-3q^{10}+\cdots\)
17298.2.a.m	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
17298.2.a.n	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
17298.2.a.o	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
17298.2.a.p	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
17298.2.a.q	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
17298.2.a.r	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
17298.2.a.s	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots\)
17298.2.a.t	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
17298.2.a.u	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
17298.2.a.v	$17298$	$2$	17298.a	1.a	$1$	$1$	$1$	$138.125$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
17298.2.a.w	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-4\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.x	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-4\)	\(-3\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.y	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.z	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{41}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.ba	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{41}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bb	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.bc	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bd	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.be	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bf	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(3\)	\(5\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.bg	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(3\)	\(5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bh	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-3\)	\(5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bi	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-3\)	\(5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.bj	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bk	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bl	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.bm	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bn	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{19}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bo	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{19}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.bp	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bq	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.br	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bs	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.bt	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.bu	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{10}) \)	not computed	✓	?				$-1$		\(2\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$
17298.2.a.bv	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(6\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bw	$17298$	$2$	17298.a	1.a	$1$	$2$	$2$	$138.125$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(6\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bx	$17298$	$2$	17298.a	1.a	$1$	$3$	$3$	$138.125$	3.3.2292.1	None	✓	?				$-1$		\(-3\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.by	$17298$	$2$	17298.a	1.a	$1$	$3$	$3$	$138.125$	3.3.2292.1	None	✓	?				$-1$		\(-3\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.bz	$17298$	$2$	17298.a	1.a	$1$	$3$	$3$	$138.125$	3.3.2292.1	None	✓	?				$-1$		\(3\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.ca	$17298$	$2$	17298.a	1.a	$1$	$3$	$3$	$138.125$	3.3.2292.1	None	✓	?				$-1$		\(3\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.cb	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{16})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.cc	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{16})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.cd	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.19225.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.ce	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.19225.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.cf	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.cg	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.ch	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.4525.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.ci	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.22592.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.cj	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.22592.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.ck	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.4525.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.cl	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(3\)	\(-11\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.cm	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(3\)	\(-11\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.cn	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{16})^+\)	not computed	✓	?				$-1$		\(-4\)	\(0\)	\(8\)	\(-8\)		$+$	$-$	$-$	$+$
17298.2.a.co	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-5\)	\(-7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.cp	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-5\)	\(-7\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.cq	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\sqrt{2}, \sqrt{5})\)	not computed	✓	?				$-1$		\(4\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$
17298.2.a.cr	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.cs	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.ct	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.8725.1	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.cu	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	4.4.8725.1	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.cv	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(7\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.cw	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.cx	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{16})^+\)	not computed	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$
17298.2.a.cy	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(7\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.cz	$17298$	$2$	17298.a	1.a	$1$	$4$	$4$	$138.125$	\(\Q(\zeta_{15})^+\)	None	✓	?				$-1$		\(4\)	\(0\)	\(7\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.da	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.\(\cdots\).1	None	✓	?	✓			$-1$		\(-8\)	\(0\)	\(-5\)	\(8\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.db	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.\(\cdots\).1	None	✓	?				$-1$		\(-8\)	\(0\)	\(-5\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.dc	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	\(\Q(\zeta_{32})^+\)	None	✓	?				$-1$		\(-8\)	\(0\)	\(8\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.dd	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.4848615424.1	not computed	✓	?				$-1$		\(-8\)	\(0\)	\(8\)	\(0\)		$+$	$+$	$-$	$-$
17298.2.a.de	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	\(\Q(\zeta_{32})^+\)	None	✓	?				$-1$		\(-8\)	\(0\)	\(8\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.df	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	\(\Q(\zeta_{32})^+\)	None	✓	?				$-1$		\(8\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.dg	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.4848615424.1	not computed	✓	?				$-1$		\(8\)	\(0\)	\(-8\)	\(0\)		$-$	$+$	$-$	$+$
17298.2.a.dh	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	\(\Q(\zeta_{32})^+\)	None	✓	?				$-1$		\(8\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.di	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	\(\Q(\zeta_{32})^+\)	not computed	✓	?				$-1$		\(8\)	\(0\)	\(0\)	\(-16\)		$-$	$-$	$+$	$+$
17298.2.a.dj	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.\(\cdots\).1	None	✓	?				$-1$		\(8\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.dk	$17298$	$2$	17298.a	1.a	$1$	$8$	$8$	$138.125$	8.8.\(\cdots\).1	None	✓	?				$-1$		\(8\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.dl	$17298$	$2$	17298.a	1.a	$1$	$12$	$12$	$138.125$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17298.2.a.dm	$17298$	$2$	17298.a	1.a	$1$	$12$	$12$	$138.125$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(-12\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17298.2.a.dn	$17298$	$2$	17298.a	1.a	$1$	$12$	$12$	$138.125$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(12\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17298.2.a.do	$17298$	$2$	17298.a	1.a	$1$	$12$	$12$	$138.125$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17298.2.a.dp	$17298$	$2$	17298.a	1.a	$1$	$16$	$16$	$138.125$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?	✓			$-1$		\(-16\)	\(0\)	\(-16\)	\(16\)		$+$	$-$	$+$	$-$
17298.2.a.dq	$17298$	$2$	17298.a	1.a	$1$	$24$	$24$	$138.125$		not computed	✓	?	✓			$-1$		\(-24\)	\(0\)	\(-16\)	\(0\)		$+$	$+$	$+$	$+$
17298.2.a.dr	$17298$	$2$	17298.a	1.a	$1$	$24$	$24$	$138.125$		not computed	✓	?	✓			$-1$		\(24\)	\(0\)	\(16\)	\(0\)		$-$	$+$	$+$	$-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(17298))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(17298)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(961))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1922))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2883))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5766))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8649))\)\(^{\oplus 2}\)