LMFDB - Space of modular forms of level 9702, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 107 $
Sturm bound:			$4032$
Trace bound:			$31$
Distinguishing $T_p$:			$5$, $13$, $17$, $19$, $23$, $29$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9702))$.

	Total	New	Old
Modular forms	2080	169	1911
Cusp forms	1953	169	1784
Eisenstein series	127	0	127

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

$2$	$3$	$7$	$11$	Fricke	Dim
$+$	$+$	$+$	$+$	$+$	$5$
$+$	$+$	$+$	$-$	$-$	$9$
$+$	$+$	$-$	$+$	$-$	$11$
$+$	$+$	$-$	$-$	$+$	$8$
$+$	$-$	$+$	$+$	$-$	$13$
$+$	$-$	$+$	$-$	$+$	$13$
$+$	$-$	$-$	$+$	$+$	$13$
$+$	$-$	$-$	$-$	$-$	$13$
$-$	$+$	$+$	$+$	$-$	$9$
$-$	$+$	$+$	$-$	$+$	$5$
$-$	$+$	$-$	$+$	$+$	$8$
$-$	$+$	$-$	$-$	$-$	$11$
$-$	$-$	$+$	$+$	$+$	$11$
$-$	$-$	$+$	$-$	$-$	$15$
$-$	$-$	$-$	$+$	$-$	$14$
$-$	$-$	$-$	$-$	$+$	$11$
Plus space				$+$	$74$
Minus space				$-$	$95$

Trace form

$ 169 q - q^{2} + 169 q^{4} - 2 q^{5} - q^{8} + O(q^{10}) $

$ 169 q - q^{2} + 169 q^{4} - 2 q^{5} - q^{8} - 2 q^{10} + q^{11} - 2 q^{13} + 169 q^{16} - 18 q^{17} - 12 q^{19} - 2 q^{20} - q^{22} - 4 q^{23} + 159 q^{25} - 14 q^{26} + 2 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} + 30 q^{37} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 52 q^{43} + q^{44} + 4 q^{47} - 39 q^{50} - 2 q^{52} - 38 q^{53} - 6 q^{55} - 50 q^{58} + 16 q^{59} - 2 q^{61} - 8 q^{62} + 169 q^{64} - 52 q^{65} + 44 q^{67} - 18 q^{68} - 20 q^{71} + 10 q^{73} - 46 q^{74} - 12 q^{76} + 80 q^{79} - 2 q^{80} - 14 q^{82} - 20 q^{83} - 76 q^{85} + 8 q^{86} - q^{88} - 6 q^{89} - 4 q^{92} + 8 q^{94} + 32 q^{95} - 46 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9702))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9702.2.a.a	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-q^{11}+\cdots$
9702.2.a.b	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-4$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}+q^{11}+\cdots$
9702.2.a.c	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-3$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+q^{11}+\cdots$
9702.2.a.d	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.e	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.f	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.g	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.h	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.i	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.j	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.k	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
9702.2.a.l	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}-5q^{13}+q^{16}+\cdots$
9702.2.a.m	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots$
9702.2.a.n	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots$
9702.2.a.o	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}+5q^{13}+q^{16}+\cdots$
9702.2.a.p	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots$
9702.2.a.q	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.r	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.s	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.t	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.u	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.v	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.w	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.x	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.y	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.z	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{11}+\cdots$
9702.2.a.ba	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots$
9702.2.a.bb	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots$
9702.2.a.bc	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-q^{11}+\cdots$
9702.2.a.bd	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots$
9702.2.a.be	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-3$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots$
9702.2.a.bf	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.bg	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots$
9702.2.a.bh	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.bi	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.bj	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{11}+\cdots$
9702.2.a.bk	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots$
9702.2.a.bl	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots$
9702.2.a.bm	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots$
9702.2.a.bn	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots$
9702.2.a.bo	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots$
9702.2.a.bp	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}-6q^{13}+q^{16}+\cdots$
9702.2.a.bq	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}-4q^{13}+q^{16}+\cdots$
9702.2.a.br	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}-q^{13}+q^{16}+\cdots$
9702.2.a.bs	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}+q^{13}+q^{16}+\cdots$
9702.2.a.bt	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}+2q^{13}+q^{16}+\cdots$
9702.2.a.bu	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots$
9702.2.a.bv	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots$
9702.2.a.bw	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
9702.2.a.bx	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.by	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.bz	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots$
9702.2.a.ca	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.cb	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.cc	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.cd	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-q^{11}+\cdots$
9702.2.a.ce	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots$
9702.2.a.cf	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots$
9702.2.a.cg	$9702$	$2$	9702.a	1.a	$1$	$1$	$1$	$77.471$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+q^{11}+\cdots$
9702.2.a.ch	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots$
9702.2.a.ci	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-4$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots$
9702.2.a.cj	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
9702.2.a.ck	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
9702.2.a.cl	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-q^{11}+\cdots$
9702.2.a.cm	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots$
9702.2.a.cn	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{10}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots$
9702.2.a.co	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}+3\beta q^{13}+\cdots$
9702.2.a.cp	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots$
9702.2.a.cq	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{11}-3\beta q^{13}+\cdots$
9702.2.a.cr	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots$
9702.2.a.cs	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots$
9702.2.a.ct	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots$
9702.2.a.cu	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.cv	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.cw	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.cx	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots$
9702.2.a.cy	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots$
9702.2.a.cz	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{7}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.da	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.db	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{7}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.dc	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{10}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.dd	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.de	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots$
9702.2.a.df	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots$
9702.2.a.dg	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.dh	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}+3\beta q^{13}+\cdots$
9702.2.a.di	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots$
9702.2.a.dj	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots$
9702.2.a.dk	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.dl	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots$
9702.2.a.dm	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{7}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots$
9702.2.a.dn	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+q^{11}-\beta q^{13}+q^{16}+\cdots$
9702.2.a.do	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots$
9702.2.a.dp	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots$
9702.2.a.dq	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots$
9702.2.a.dr	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{7}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots$
9702.2.a.ds	$9702$	$2$	9702.a	1.a	$1$	$2$	$2$	$77.471$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$2$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots$
9702.2.a.dt	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.621.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+\beta _{2}q^{10}+\cdots$
9702.2.a.du	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.621.1	None	✓	$1$	$1$	$-3$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{8}-\beta _{2}q^{10}+\cdots$
9702.2.a.dv	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.2700.1	None	✓	$1$	$1$	$-3$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{8}+\beta _{1}q^{10}+\cdots$
9702.2.a.dw	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.2700.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots$
9702.2.a.dx	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.1304.1	None	✓	$1$	$0$	$-3$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{2})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.dy	$9702$	$2$	9702.a	1.a	$1$	$3$	$3$	$77.471$	3.3.1304.1	None	✓	$1$	$0$	$3$	$0$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.dz	$9702$	$2$	9702.a	1.a	$1$	$4$	$4$	$77.471$	4.4.4352.1	None	✓	$1$	$0$	$-4$	$0$	$-4$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{3})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
9702.2.a.ea	$9702$	$2$	9702.a	1.a	$1$	$4$	$4$	$77.471$	4.4.4352.1	None	✓	$1$	$0$	$-4$	$0$	$4$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{3})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
9702.2.a.eb	$9702$	$2$	9702.a	1.a	$1$	$4$	$4$	$77.471$	4.4.14336.1	None	✓	$1$	$0$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots$
9702.2.a.ec	$9702$	$2$	9702.a	1.a	$1$	$4$	$4$	$77.471$	4.4.14336.1	None	✓	$1$	$0$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9702))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 107 \)
Sturm bound:			\(4032\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\), \(19\), \(23\), \(29\)

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(9\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(13\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(13\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(8\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(11\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(11\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(15\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(14\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(11\)
Plus space				\(+\)	\(74\)
Minus space				\(-\)	\(95\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9702))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9702))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	9702.2.a

Level	$9702$
Weight	$2$
Character orbit	9702.a
Rep. character	$\chi_{9702}(1,\cdot)$
Character field	$\Q$
Dimension	$169$
Newform subspaces	$107$
Sturm bound	$4032$
Trace bound	$31$