Space of modular forms of level 17400, weight 2, and trivial character

• Label: 17400.2.a
• Level: $17400$
• Weight: $2$
• Character orbit: 17400.a
• Rep. character: $\chi_{17400}(1,\cdot)$
• Character field: $\Q$
• Dimension: $266$
• Newform subspaces: $86$
• Sturm bound: $7200$

Defining parameters

Level:	$N$	$=$	$17400 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	17400.a (trivial)
Character field:			$\Q$
Newform subspaces:			$86$
Sturm bound:			$7200$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(17400))$.

	Total	New	Old
Modular forms	3648	266	3382
Cusp forms	3553	266	3287
Eisenstein series	95	0	95

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

$2$	$3$	$5$	$29$	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$	$+$	$+$		$213$	$15$	$198$		$208$	$15$	$193$		$5$	$0$	$5$
$+$	$+$	$+$	$-$	$-$		$240$	$15$	$225$		$234$	$15$	$219$		$6$	$0$	$6$
$+$	$+$	$-$	$+$	$-$		$239$	$19$	$220$		$233$	$19$	$214$		$6$	$0$	$6$
$+$	$+$	$-$	$-$	$+$		$218$	$17$	$201$		$212$	$17$	$195$		$6$	$0$	$6$
$+$	$-$	$+$	$+$	$-$		$243$	$18$	$225$		$237$	$18$	$219$		$6$	$0$	$6$
$+$	$-$	$+$	$-$	$+$		$216$	$15$	$201$		$210$	$15$	$195$		$6$	$0$	$6$
$+$	$-$	$-$	$+$	$+$		$217$	$15$	$202$		$211$	$15$	$196$		$6$	$0$	$6$
$+$	$-$	$-$	$-$	$-$		$238$	$19$	$219$		$232$	$19$	$213$		$6$	$0$	$6$
$-$	$+$	$+$	$+$	$-$		$225$	$15$	$210$		$219$	$15$	$204$		$6$	$0$	$6$
$-$	$+$	$+$	$-$	$+$		$234$	$15$	$219$		$228$	$15$	$213$		$6$	$0$	$6$
$-$	$+$	$-$	$+$	$+$		$235$	$17$	$218$		$229$	$17$	$212$		$6$	$0$	$6$
$-$	$+$	$-$	$-$	$-$		$220$	$19$	$201$		$214$	$19$	$195$		$6$	$0$	$6$
$-$	$-$	$+$	$+$	$+$		$231$	$15$	$216$		$225$	$15$	$210$		$6$	$0$	$6$
$-$	$-$	$+$	$-$	$-$		$222$	$18$	$204$		$216$	$18$	$198$		$6$	$0$	$6$
$-$	$-$	$-$	$+$	$-$		$221$	$19$	$202$		$215$	$19$	$196$		$6$	$0$	$6$
$-$	$-$	$-$	$-$	$+$		$236$	$15$	$221$		$230$	$15$	$215$		$6$	$0$	$6$
Plus space				$+$		$1800$	$124$	$1676$		$1753$	$124$	$1629$		$47$	$0$	$47$
Minus space				$-$		$1848$	$142$	$1706$		$1800$	$142$	$1658$		$48$	$0$	$48$

Trace form

266 * q + 2 * q^3 + 4 * q^7 + 266 * q^9 + 8 * q^11 + 4 * q^13 + 8 * q^21 - 24 * q^23 + 2 * q^27 + 4 * q^31 + 8 * q^37 + 4 * q^39 - 32 * q^41 + 16 * q^43 + 40 * q^47 + 246 * q^49 - 8 * q^53 + 12 * q^57 + 28 * q^59 + 16 * q^61 + 4 * q^63 + 16 * q^67 + 8 * q^69 + 32 * q^71 + 4 * q^73 - 16 * q^77 + 92 * q^79 + 266 * q^81 - 28 * q^83 - 24 * q^89 + 88 * q^91 - 20 * q^93 + 20 * q^97 + 8 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(17400))$ 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	5	29
17400.2.a.a	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-4$		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
17400.2.a.b	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-4$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
17400.2.a.c	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-3$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
17400.2.a.d	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-3$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+q^{11}-q^{13}-3q^{17}+\cdots$
17400.2.a.e	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-2$		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
17400.2.a.f	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-2$		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-4q^{13}-2q^{17}+\cdots$
17400.2.a.g	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-2$		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
17400.2.a.h	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-2$		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
17400.2.a.i	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots$
17400.2.a.j	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
17400.2.a.k	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$0$		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{11}+2q^{13}+6q^{17}+\cdots$
17400.2.a.l	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$0$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{13}+2q^{17}-q^{27}+\cdots$
17400.2.a.m	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$0$		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}+4q^{13}+6q^{17}+\cdots$
17400.2.a.n	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}+7q^{13}+\cdots$
17400.2.a.o	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$2$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
17400.2.a.p	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$2$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
17400.2.a.q	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$2$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
17400.2.a.r	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$2$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+3q^{11}+6q^{13}+\cdots$
17400.2.a.s	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$2$		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots$
17400.2.a.t	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$3$		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots$
17400.2.a.u	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$4$		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
17400.2.a.v	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$4$		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
17400.2.a.w	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$5$		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
17400.2.a.x	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-4$		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
17400.2.a.y	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-4$		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
17400.2.a.z	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-3$		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
17400.2.a.ba	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-3$		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+q^{11}-q^{13}+q^{17}+\cdots$
17400.2.a.bb	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-2$		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots$
17400.2.a.bc	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-2$		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{17}+\cdots$
17400.2.a.bd	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-2$		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
17400.2.a.be	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$0$		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+4q^{13}+2q^{17}+6q^{19}+\cdots$
17400.2.a.bf	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$0$		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2q^{11}-4q^{13}-6q^{17}+\cdots$
17400.2.a.bg	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+q^{17}+\cdots$
17400.2.a.bh	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-q^{11}+3q^{13}-q^{17}+\cdots$
17400.2.a.bi	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$2$		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
17400.2.a.bj	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$2$		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+4q^{13}+2q^{17}+\cdots$
17400.2.a.bk	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$2$		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
17400.2.a.bl	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$2$		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots$
17400.2.a.bm	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$3$		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
17400.2.a.bn	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$3$		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$
17400.2.a.bo	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$3$		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots$
17400.2.a.bp	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$4$		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
17400.2.a.bq	$17400$	$2$	17400.a	1.a	$1$	$1$	$1$	$138.940$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$4$		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
17400.2.a.br	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{5})$	None	✓	?				$-1$		$0$	$-2$	$0$	$-4$		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.bs	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{41})$	None	✓	?				$-1$		$0$	$-2$	$0$	$-3$		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.bt	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{17})$	None	✓	?				$-1$		$0$	$-2$	$0$	$-1$		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.bu	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{33})$	None	✓	?				$-1$		$0$	$-2$	$0$	$1$		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.bv	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{17})$	None	✓	?				$-1$		$0$	$-2$	$0$	$3$		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.bw	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{33})$	None	✓	?				$-1$		$0$	$2$	$0$	$-4$		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.bx	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{17})$	None	✓	?				$-1$		$0$	$2$	$0$	$-3$		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.by	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{17})$	None	✓	?				$-1$		$0$	$2$	$0$	$0$		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.bz	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{5})$	None	✓	?				$-1$		$0$	$2$	$0$	$4$		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.ca	$17400$	$2$	17400.a	1.a	$1$	$2$	$2$	$138.940$	$\Q(\sqrt{17})$	None	✓	?				$-1$		$0$	$2$	$0$	$5$		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cb	$17400$	$2$	17400.a	1.a	$1$	$3$	$3$	$138.940$	3.3.961.1	None	✓	?				$-1$		$0$	$-3$	$0$	$-4$		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.cc	$17400$	$2$	17400.a	1.a	$1$	$3$	$3$	$138.940$	3.3.940.1	None	✓	?				$-1$		$0$	$-3$	$0$	$-2$		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cd	$17400$	$2$	17400.a	1.a	$1$	$3$	$3$	$138.940$	3.3.229.1	None	✓	?				$-1$		$0$	$3$	$0$	$-1$		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.ce	$17400$	$2$	17400.a	1.a	$1$	$3$	$3$	$138.940$	3.3.229.1	None	✓	?				$-1$		$0$	$3$	$0$	$1$		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.cf	$17400$	$2$	17400.a	1.a	$1$	$3$	$3$	$138.940$	3.3.940.1	None	✓	?				$-1$		$0$	$3$	$0$	$2$		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cg	$17400$	$2$	17400.a	1.a	$1$	$4$	$4$	$138.940$	4.4.69272.1	None	✓	?				$-1$		$0$	$-4$	$0$	$-1$		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.ch	$17400$	$2$	17400.a	1.a	$1$	$4$	$4$	$138.940$	4.4.58397.1	None	✓	?				$-1$		$0$	$-4$	$0$	$3$		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.ci	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.21913725.1	None	✓	?				$-1$		$0$	$-5$	$0$	$-2$		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cj	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.18239409.1	None	✓	?	✓			$-1$		$0$	$-5$	$0$	$-1$		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.ck	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.1752165.1	None	✓	?	✓			$-1$		$0$	$-5$	$0$	$4$		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cl	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.1752165.1	None	✓	?				$-1$		$0$	$5$	$0$	$-4$		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cm	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.18396776.1	None	✓	?				$-1$		$0$	$5$	$0$	$-1$		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cn	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.1025428.1	None	✓	?				$-1$		$0$	$5$	$0$	$-1$		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.co	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.18239409.1	None	✓	?				$-1$		$0$	$5$	$0$	$1$		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.cp	$17400$	$2$	17400.a	1.a	$1$	$5$	$5$	$138.940$	5.5.21913725.1	None	✓	?				$-1$		$0$	$5$	$0$	$2$		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cq	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.121002181.1	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$-7$		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cr	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.62452821.1	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$3$		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.cs	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.70558128.1	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$4$		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.ct	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.70558128.1	None	✓	?	✓			$-1$		$0$	$6$	$0$	$-4$		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cu	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.62452821.1	None	✓	?				$-1$		$0$	$6$	$0$	$-3$		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.cv	$17400$	$2$	17400.a	1.a	$1$	$6$	$6$	$138.940$	6.6.121002181.1	None	✓	?				$-1$		$0$	$6$	$0$	$7$		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cw	$17400$	$2$	17400.a	1.a	$1$	$7$	$7$	$138.940$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?				$-1$		$0$	$-7$	$0$	$2$		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.cx	$17400$	$2$	17400.a	1.a	$1$	$7$	$7$	$138.940$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?				$-1$		$0$	$-7$	$0$	$4$		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.cy	$17400$	$2$	17400.a	1.a	$1$	$7$	$7$	$138.940$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$-4$		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
17400.2.a.cz	$17400$	$2$	17400.a	1.a	$1$	$7$	$7$	$138.940$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$-2$		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.da	$17400$	$2$	17400.a	1.a	$1$	$8$	$8$	$138.940$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$0$	$-8$	$0$	$-2$		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.db	$17400$	$2$	17400.a	1.a	$1$	$8$	$8$	$138.940$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$0$	$-8$	$0$	$2$		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.dc	$17400$	$2$	17400.a	1.a	$1$	$8$	$8$	$138.940$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$0$	$8$	$0$	$-2$		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
17400.2.a.dd	$17400$	$2$	17400.a	1.a	$1$	$8$	$8$	$138.940$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$0$	$8$	$0$	$2$		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.de	$17400$	$2$	17400.a	1.a	$1$	$11$	$11$	$138.940$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-11$	$0$	$-4$		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
17400.2.a.df	$17400$	$2$	17400.a	1.a	$1$	$11$	$11$	$138.940$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-11$	$0$	$0$		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.dg	$17400$	$2$	17400.a	1.a	$1$	$11$	$11$	$138.940$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$11$	$0$	$0$		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
17400.2.a.dh	$17400$	$2$	17400.a	1.a	$1$	$11$	$11$	$138.940$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$11$	$0$	$4$		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(17400))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(17400)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(15))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(20))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(24))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(29))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(30))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(40))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(50))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(58))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(75))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(87))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(100))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(116))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(120))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(145))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(150))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(174))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(200))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(232))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(290))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(300))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(348))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(435))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(580))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(600))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(696))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(725))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(870))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1160))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1450))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1740))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(2175))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(2900))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(3480))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(4350))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(5800))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(8700))$$^{\oplus 2}$