Space of modular forms of level 5202, weight 2, and trivial character

• Label: 5202.2.a
• Level: $5202$
• Weight: $2$
• Character orbit: 5202.a
• Rep. character: $\chi_{5202}(1,\cdot)$
• Character field: $\Q$
• Dimension: $112$
• Newform subspaces: $50$
• Sturm bound: $1836$
• Trace bound: $19$

Defining parameters

Level:	$N$	$=$	$5202 = 2 \cdot 3^{2} \cdot 17^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	5202.a (trivial)
Character field:			$\Q$
Newform subspaces:			$50$
Sturm bound:			$1836$
Trace bound:			$19$
Distinguishing $T_p$:			$5$, $7$, $23$, $47$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5202))$.

	Total	New	Old
Modular forms	990	112	878
Cusp forms	847	112	735
Eisenstein series	143	0	143

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

$2$	$3$	$17$	Fricke	Dim
$+$	$+$	$+$	$+$	$13$
$+$	$+$	$-$	$-$	$9$
$+$	$-$	$+$	$-$	$18$
$+$	$-$	$-$	$+$	$16$
$-$	$+$	$+$	$-$	$13$
$-$	$+$	$-$	$+$	$9$
$-$	$-$	$+$	$+$	$14$
$-$	$-$	$-$	$-$	$20$
Plus space			$+$	$52$
Minus space			$-$	$60$

Trace form

112 * q + 112 * q^4 - 6 * q^5 - 4 * q^7 - 2 * q^10 + 2 * q^11 - 4 * q^14 + 112 * q^16 - 4 * q^19 - 6 * q^20 - 2 * q^22 + 120 * q^25 + 8 * q^26 - 4 * q^28 - 14 * q^29 + 4 * q^31 + 4 * q^35 + 18 * q^37 - 4 * q^38 - 2 * q^40 + 12 * q^41 + 4 * q^43 + 2 * q^44 + 24 * q^46 + 12 * q^47 + 108 * q^49 - 16 * q^50 + 4 * q^53 + 48 * q^55 - 4 * q^56 + 6 * q^58 + 4 * q^59 + 26 * q^61 + 20 * q^62 + 112 * q^64 + 28 * q^65 + 12 * q^67 + 28 * q^70 + 24 * q^73 - 10 * q^74 - 4 * q^76 - 24 * q^77 - 8 * q^79 - 6 * q^80 + 4 * q^82 + 8 * q^83 + 24 * q^86 - 2 * q^88 - 40 * q^89 + 24 * q^91 + 12 * q^94 - 24 * q^95 + 20 * q^97 + 8 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5202))$ 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	17
5202.2.a.a	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.i	$1$	$1$	$-1$	$0$	$-4$	$3$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}+3q^{7}-q^{8}+4q^{10}+\cdots$
5202.2.a.b	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.k	$1$	$0$	$-1$	$0$	$-3$	$4$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+4q^{7}-q^{8}+3q^{10}+\cdots$
5202.2.a.c	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				102.2.a.c	$1$	$0$	$-1$	$0$	$-2$	$0$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-4q^{11}+\cdots$
5202.2.a.d	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				34.2.a.a	$1$	$0$	$-1$	$0$	$0$	$4$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
5202.2.a.e	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.k	$1$	$1$	$-1$	$0$	$3$	$-4$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots$
5202.2.a.f	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.i	$1$	$0$	$-1$	$0$	$4$	$-3$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-3q^{7}-q^{8}-4q^{10}+\cdots$
5202.2.a.g	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				102.2.a.a	$1$	$1$	$1$	$0$	$-4$	$2$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+2q^{7}+q^{8}-4q^{10}+\cdots$
5202.2.a.h	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				102.2.b.a	$1$	$1$	$1$	$0$	$-2$	$2$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots$
5202.2.a.i	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.a	$1$	$1$	$1$	$0$	$-1$	$-4$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
5202.2.a.j	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				102.2.a.b	$1$	$1$	$1$	$0$	$0$	$-2$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{13}-2q^{14}+\cdots$
5202.2.a.k	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.c	$1$	$0$	$1$	$0$	$0$	$-1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{13}-q^{14}+\cdots$
5202.2.a.l	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.c	$1$	$1$	$1$	$0$	$0$	$1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
5202.2.a.m	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				1734.2.a.a	$1$	$0$	$1$	$0$	$1$	$4$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
5202.2.a.n	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓				102.2.b.a	$1$	$1$	$1$	$0$	$2$	$-2$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
5202.2.a.o	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				102.2.f.a	$1$	$0$	$-2$	$0$	$-4$	$4$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+\cdots$
5202.2.a.p	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33})$	None	✓	✓			5202.2.a.p	$1$	$1$	$-2$	$0$	$-3$	$-1$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}-\beta q^{7}-q^{8}+\cdots$
5202.2.a.q	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{6})$	None	✓				306.2.a.e	$1$	$1$	$-2$	$0$	$0$	$-4$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(-2+\beta )q^{7}-q^{8}+\cdots$
5202.2.a.r	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.g.c	$2$	$1$	$-2$	$0$	$0$	$0$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-\beta q^{7}-q^{8}-2\beta q^{10}+\cdots$
5202.2.a.s	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.g.a	$2$	$1$	$-2$	$0$	$0$	$0$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-3\beta q^{7}-q^{8}+\cdots$
5202.2.a.t	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.b.b	$2$	$1$	$-2$	$0$	$0$	$0$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
5202.2.a.u	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				34.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-\beta q^{11}+\cdots$
5202.2.a.v	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				34.2.c.a	$2$	$0$	$-2$	$0$	$0$	$0$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+2\beta q^{7}-q^{8}+\cdots$
5202.2.a.w	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33})$	None	✓	✓			5202.2.a.p	$1$	$0$	$-2$	$0$	$3$	$1$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+\beta q^{7}-q^{8}+\cdots$
5202.2.a.x	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				102.2.f.a	$1$	$0$	$-2$	$0$	$4$	$-4$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}+(-2+2\beta )q^{7}+\cdots$
5202.2.a.y	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33})$	None	✓	✓			5202.2.a.p	$1$	$1$	$2$	$0$	$-3$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}+\beta q^{7}+q^{8}+\cdots$
5202.2.a.z	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{6})$	None	✓				306.2.a.e	$1$	$0$	$2$	$0$	$0$	$-4$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+(-2-\beta )q^{7}+q^{8}+\cdots$
5202.2.a.ba	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.g.c	$2$	$0$	$2$	$0$	$0$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+\beta q^{7}+q^{8}+2\beta q^{10}+\cdots$
5202.2.a.bb	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				34.2.c.b	$2$	$1$	$2$	$0$	$0$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-4\beta q^{11}+\cdots$
5202.2.a.bc	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.g.a	$2$	$0$	$2$	$0$	$0$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+3\beta q^{7}+q^{8}+\cdots$
5202.2.a.bd	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2})$	None	✓				306.2.b.b	$2$	$0$	$2$	$0$	$0$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+3\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
5202.2.a.be	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33})$	None	✓	✓			5202.2.a.p	$1$	$0$	$2$	$0$	$3$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots$
5202.2.a.bf	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				1734.2.a.r	$1$	$1$	$-3$	$0$	$-6$	$-3$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bg	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				578.2.a.g	$1$	$0$	$-3$	$0$	$-6$	$3$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2-\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bh	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		5202.2.a.bh	$1$	$1$	$-3$	$0$	$-6$	$3$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2-\beta _{1})q^{5}+q^{7}-q^{8}+\cdots$
5202.2.a.bi	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				578.2.a.g	$1$	$1$	$-3$	$0$	$6$	$-3$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bj	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	✓			5202.2.a.bh	$1$	$0$	$-3$	$0$	$6$	$-3$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}-q^{7}-q^{8}+\cdots$
5202.2.a.bk	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				1734.2.a.r	$1$	$0$	$-3$	$0$	$6$	$3$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bl	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	✓			5202.2.a.bh	$1$	$1$	$3$	$0$	$-6$	$-3$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2-\beta _{1})q^{5}-q^{7}+q^{8}+\cdots$
5202.2.a.bm	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				1734.2.a.p	$1$	$1$	$3$	$0$	$-6$	$3$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bn	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				578.2.a.e	$1$	$1$	$3$	$0$	$0$	$-9$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots$
5202.2.a.bo	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				578.2.a.e	$1$	$0$	$3$	$0$	$0$	$9$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(3+\beta _{2})q^{7}+\cdots$
5202.2.a.bp	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓				1734.2.a.p	$1$	$0$	$3$	$0$	$6$	$-3$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bq	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		5202.2.a.bh	$1$	$0$	$3$	$0$	$6$	$3$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta _{1})q^{5}+q^{7}+q^{8}+\cdots$
5202.2.a.br	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓				102.2.h.a	$1$	$1$	$-4$	$0$	$0$	$-8$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$
5202.2.a.bs	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓		✓		306.2.l.a	$2$	$0$	$-4$	$0$	$0$	$0$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+2\beta _{3}q^{7}-q^{8}+\cdots$
5202.2.a.bt	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓				102.2.h.a	$1$	$1$	$-4$	$0$	$0$	$8$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots$
5202.2.a.bu	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓				102.2.h.b	$1$	$0$	$4$	$0$	$-8$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bv	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓		✓		306.2.l.a	$2$	$1$	$4$	$0$	$0$	$0$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-2\beta _{3}q^{7}+q^{8}+\cdots$
5202.2.a.bw	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓				34.2.d.a	$2$	$0$	$4$	$0$	$0$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+2\beta _{3}q^{7}+q^{8}+\cdots$
5202.2.a.bx	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓				102.2.h.b	$1$	$0$	$4$	$0$	$8$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5202))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(5202)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(17))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(34))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(51))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(102))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(153))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(289))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(306))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(578))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(867))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1734))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(2601))$$^{\oplus 2}$