LMFDB - Space of modular forms of level 9350, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9350 = 2 \cdot 5^{2} \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9350.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 85 $
Sturm bound:			$3240$
Trace bound:			$11$
Distinguishing $T_p$:			$3$, $7$, $13$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9350))$.

	Total	New	Old
Modular forms	1644	256	1388
Cusp forms	1597	256	1341
Eisenstein series	47	0	47

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

$2$	$5$	$11$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$5$	$11$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$93$	$15$	$78$	$91$	$15$	$76$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$-$	$111$	$16$	$95$	$108$	$16$	$92$	$3$	$0$	$3$
$+$	$+$	$-$	$+$	$-$	$108$	$16$	$92$	$105$	$16$	$89$	$3$	$0$	$3$
$+$	$+$	$-$	$-$	$+$	$96$	$13$	$83$	$93$	$13$	$80$	$3$	$0$	$3$
$+$	$-$	$+$	$+$	$-$	$109$	$19$	$90$	$106$	$19$	$87$	$3$	$0$	$3$
$+$	$-$	$+$	$-$	$+$	$98$	$15$	$83$	$95$	$15$	$80$	$3$	$0$	$3$
$+$	$-$	$-$	$+$	$+$	$101$	$13$	$88$	$98$	$13$	$85$	$3$	$0$	$3$
$+$	$-$	$-$	$-$	$-$	$106$	$21$	$85$	$103$	$21$	$82$	$3$	$0$	$3$
$-$	$+$	$+$	$+$	$-$	$105$	$16$	$89$	$102$	$16$	$86$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$+$	$102$	$12$	$90$	$99$	$12$	$87$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$+$	$99$	$13$	$86$	$96$	$13$	$83$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$-$	$108$	$19$	$89$	$105$	$19$	$86$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$+$	$104$	$15$	$89$	$101$	$15$	$86$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$-$	$100$	$21$	$79$	$97$	$21$	$76$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$-$	$103$	$21$	$82$	$100$	$21$	$79$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$+$	$101$	$11$	$90$	$98$	$11$	$87$	$3$	$0$	$3$
Plus space				$+$	$794$	$107$	$687$	$771$	$107$	$664$	$23$	$0$	$23$
Minus space				$-$	$850$	$149$	$701$	$826$	$149$	$677$	$24$	$0$	$24$

Trace form

$ 256 q + 256 q^{4} - 8 q^{6} + 16 q^{7} + 252 q^{9} - 2 q^{11} + 16 q^{13} - 16 q^{14} + 256 q^{16} - 16 q^{18} + 48 q^{19} + 24 q^{21} + 2 q^{22} - 32 q^{23} - 8 q^{24} + 4 q^{26} + 16 q^{28} - 24 q^{29}+ \cdots + 54 q^{99}+O(q^{100}) $

256 * q + 256 * q^4 - 8 * q^6 + 16 * q^7 + 252 * q^9 - 2 * q^11 + 16 * q^13 - 16 * q^14 + 256 * q^16 - 16 * q^18 + 48 * q^19 + 24 * q^21 + 2 * q^22 - 32 * q^23 - 8 * q^24 + 4 * q^26 + 16 * q^28 - 24 * q^29 + 40 * q^31 - 4 * q^33 - 4 * q^34 + 252 * q^36 + 24 * q^37 + 4 * q^38 + 40 * q^39 + 8 * q^41 + 16 * q^43 - 2 * q^44 - 16 * q^46 + 12 * q^47 + 300 * q^49 + 16 * q^52 - 32 * q^54 - 16 * q^56 + 8 * q^57 + 8 * q^58 - 16 * q^59 + 40 * q^61 + 16 * q^62 + 40 * q^63 + 256 * q^64 + 72 * q^67 + 56 * q^69 + 56 * q^71 - 16 * q^72 + 64 * q^73 + 8 * q^74 + 48 * q^76 + 4 * q^77 - 8 * q^78 + 64 * q^79 + 304 * q^81 + 24 * q^82 + 40 * q^83 + 24 * q^84 + 20 * q^86 + 48 * q^87 + 2 * q^88 + 44 * q^89 + 128 * q^91 - 32 * q^92 + 32 * q^93 - 8 * q^96 + 16 * q^97 + 24 * q^98 + 54 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9350))$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9350.2.a.a	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.a	$1$	$1$	$-1$	$-2$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots$
9350.2.a.b	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.b.a	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
9350.2.a.c	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.b.b	$1$	$0$	$-1$	$-2$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
9350.2.a.d	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.d	$1$	$1$	$-1$	$-2$	$0$	$5$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+5q^{7}-q^{8}+\cdots$
9350.2.a.e	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.i	$1$	$1$	$-1$	$-1$	$0$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
9350.2.a.f	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.f	$1$	$2$	$-1$	$-1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
9350.2.a.g	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.g	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
9350.2.a.h	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.h	$1$	$1$	$-1$	$1$	$0$	$-3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
9350.2.a.i	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.i	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
9350.2.a.j	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.j	$1$	$0$	$-1$	$1$	$0$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
9350.2.a.k	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.h	$1$	$0$	$-1$	$1$	$0$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
9350.2.a.l	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.l	$1$	$0$	$-1$	$1$	$0$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
9350.2.a.m	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.m	$1$	$0$	$-1$	$2$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots$
9350.2.a.n	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.n	$1$	$0$	$-1$	$2$	$0$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots$
9350.2.a.o	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.o	$1$	$1$	$-1$	$2$	$0$	$2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+2q^{7}-q^{8}+\cdots$
9350.2.a.p	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.g	$1$	$0$	$-1$	$3$	$0$	$4$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots$
9350.2.a.q	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.q	$1$	$0$	$-1$	$3$	$0$	$5$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+5q^{7}-q^{8}+\cdots$
9350.2.a.r	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.q	$1$	$1$	$1$	$-3$	$0$	$-5$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}-5q^{7}+q^{8}+\cdots$
9350.2.a.s	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.o	$1$	$0$	$1$	$-2$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-2q^{7}+q^{8}+\cdots$
9350.2.a.t	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.m	$1$	$1$	$1$	$-2$	$0$	$2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots$
9350.2.a.u	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.n	$1$	$1$	$1$	$-2$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots$
9350.2.a.v	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.l	$1$	$1$	$1$	$-1$	$0$	$-3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots$
9350.2.a.w	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.f	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
9350.2.a.x	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.i	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
9350.2.a.y	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.j	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
9350.2.a.z	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.h	$1$	$0$	$1$	$-1$	$0$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots$
9350.2.a.ba	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.e	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots$
9350.2.a.bb	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.c	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-q^{11}+6q^{13}+\cdots$
9350.2.a.bc	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				374.2.a.a	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{11}+\cdots$
9350.2.a.bd	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.d	$1$	$1$	$1$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}-3q^{9}+q^{11}+\cdots$
9350.2.a.be	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.g	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
9350.2.a.bf	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.f	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
9350.2.a.bg	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.b	$1$	$1$	$1$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
9350.2.a.bh	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.d	$1$	$0$	$1$	$2$	$0$	$-5$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-5q^{7}+q^{8}+\cdots$
9350.2.a.bi	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.b.a	$1$	$1$	$1$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
9350.2.a.bj	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.b.b	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
9350.2.a.bk	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓	✓			9350.2.a.a	$1$	$0$	$1$	$2$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots$
9350.2.a.bl	$9350$	$2$	9350.a	1.a	$1$	$1$	$1$	$74.660$	$\Q$	None	✓				1870.2.a.a	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
9350.2.a.bm	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{73}) $	None	✓	✓			9350.2.a.bm	$1$	$0$	$-2$	$-2$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
9350.2.a.bn	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{17}) $	None	✓				1870.2.a.m	$1$	$1$	$-2$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+(1+\cdots)q^{9}+\cdots$
9350.2.a.bo	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{7}) $	None	✓	✓			9350.2.a.bo	$1$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-\beta q^{7}-q^{8}+\cdots$
9350.2.a.bp	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{2}) $	None	✓	✓			9350.2.a.bp	$1$	$1$	$-2$	$2$	$0$	$-6$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
9350.2.a.bq	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{2}) $	None	✓				1870.2.a.l	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
9350.2.a.br	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{2}) $	None	✓	✓			9350.2.a.bp	$1$	$0$	$2$	$-2$	$0$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
9350.2.a.bs	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{3}) $	None	✓				1870.2.a.k	$1$	$1$	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots$
9350.2.a.bt	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{7}) $	None	✓	✓			9350.2.a.bo	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{8}+\cdots$
9350.2.a.bu	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{73}) $	None	✓	✓			9350.2.a.bm	$1$	$1$	$2$	$2$	$0$	$-2$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
9350.2.a.bv	$9350$	$2$	9350.a	1.a	$1$	$2$	$2$	$74.660$	$\Q(\sqrt{2}) $	None	✓				1870.2.a.j	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
9350.2.a.bw	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.257.1	None	✓				374.2.a.c	$1$	$0$	$-3$	$-3$	$0$	$-7$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots$
9350.2.a.bx	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓	✓			9350.2.a.bx	$1$	$0$	$-3$	$-3$	$0$	$3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots$
9350.2.a.by	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.940.1	None	✓				1870.2.a.r	$1$	$0$	$-3$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{2})q^{7}+\cdots$
9350.2.a.bz	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓	✓			9350.2.a.bz	$1$	$0$	$-3$	$3$	$0$	$5$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots$
9350.2.a.ca	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓				1870.2.a.q	$1$	$0$	$-3$	$3$	$0$	$6$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots$
9350.2.a.cb	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.756.1	None	✓		✓		1870.2.a.p	$1$	$1$	$3$	$-3$	$0$	$-6$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cc	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓	✓			9350.2.a.bz	$1$	$1$	$3$	$-3$	$0$	$-5$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots$
9350.2.a.cd	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.564.1	None	✓				1870.2.a.n	$1$	$1$	$3$	$-1$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
9350.2.a.ce	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓				1870.2.a.o	$1$	$0$	$3$	$-1$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
9350.2.a.cf	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.785.1	None	✓				374.2.a.b	$1$	$0$	$3$	$1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
9350.2.a.cg	$9350$	$2$	9350.a	1.a	$1$	$3$	$3$	$74.660$	3.3.148.1	None	✓	✓			9350.2.a.bx	$1$	$1$	$3$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots$
9350.2.a.ch	$9350$	$2$	9350.a	1.a	$1$	$4$	$4$	$74.660$	4.4.17428.1	None	✓				1870.2.a.t	$1$	$0$	$-4$	$-3$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.ci	$9350$	$2$	9350.a	1.a	$1$	$4$	$4$	$74.660$	4.4.25492.1	None	✓				1870.2.a.u	$1$	$1$	$-4$	$-3$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots$
9350.2.a.cj	$9350$	$2$	9350.a	1.a	$1$	$4$	$4$	$74.660$	4.4.17417.1	None	✓				374.2.a.e	$1$	$0$	$-4$	$-1$	$0$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
9350.2.a.ck	$9350$	$2$	9350.a	1.a	$1$	$4$	$4$	$74.660$	4.4.23252.1	None	✓				1870.2.a.s	$1$	$1$	$-4$	$3$	$0$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cl	$9350$	$2$	9350.a	1.a	$1$	$4$	$4$	$74.660$	4.4.55585.1	None	✓				374.2.a.d	$1$	$0$	$4$	$-1$	$0$	$-1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{2}+\beta _{3})q^{7}+\cdots$
9350.2.a.cm	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.3484752.1	None	✓	✓	✓		9350.2.a.cm	$1$	$1$	$-5$	$-4$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cn	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.815952.1	None	✓	✓			9350.2.a.cn	$1$	$1$	$-5$	$1$	$0$	$-7$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-1+\cdots)q^{7}+\cdots$
9350.2.a.co	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.126032.1	None	✓				1870.2.b.c	$1$	$1$	$-5$	$1$	$0$	$4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
9350.2.a.cp	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.2054224.1	None	✓	✓	✓		9350.2.a.cp	$1$	$0$	$-5$	$3$	$0$	$5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cq	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.2118096.1	None	✓	✓			9350.2.a.cq	$1$	$0$	$-5$	$3$	$0$	$7$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cr	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.2118096.1	None	✓	✓	✓		9350.2.a.cq	$1$	$1$	$5$	$-3$	$0$	$-7$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.cs	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.2054224.1	None	✓	✓			9350.2.a.cp	$1$	$1$	$5$	$-3$	$0$	$-5$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
9350.2.a.ct	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.126032.1	None	✓				1870.2.b.c	$1$	$1$	$5$	$-1$	$0$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
9350.2.a.cu	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.815952.1	None	✓	✓	✓		9350.2.a.cn	$1$	$0$	$5$	$-1$	$0$	$7$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(1+\beta _{4})q^{7}+\cdots$
9350.2.a.cv	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.3102944.1	None	✓				1870.2.a.v	$1$	$0$	$5$	$1$	$0$	$8$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(2-\beta _{2}+\cdots)q^{7}+\cdots$
9350.2.a.cw	$9350$	$2$	9350.a	1.a	$1$	$5$	$5$	$74.660$	5.5.3484752.1	None	✓	✓			9350.2.a.cm	$1$	$0$	$5$	$4$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots$
9350.2.a.cx	$9350$	$2$	9350.a	1.a	$1$	$6$	$6$	$74.660$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		9350.2.a.cx	$1$	$1$	$-6$	$-1$	$0$	$-8$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
9350.2.a.cy	$9350$	$2$	9350.a	1.a	$1$	$6$	$6$	$74.660$	6.6.92511952.1	None	✓	✓	✓		9350.2.a.cy	$1$	$1$	$-6$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{2}-\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{6}+\cdots$
9350.2.a.cz	$9350$	$2$	9350.a	1.a	$1$	$6$	$6$	$74.660$	6.6.92511952.1	None	✓	✓	✓		9350.2.a.cy	$1$	$0$	$6$	$1$	$0$	$-1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{2}+\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
9350.2.a.da	$9350$	$2$	9350.a	1.a	$1$	$6$	$6$	$74.660$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			9350.2.a.cx	$1$	$0$	$6$	$1$	$0$	$8$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1-\beta _{5})q^{7}+\cdots$
9350.2.a.db	$9350$	$2$	9350.a	1.a	$1$	$7$	$7$	$74.660$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1870.2.b.d	$1$	$1$	$-7$	$3$	$0$	$4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1-\beta _{3}+\cdots)q^{7}+\cdots$
9350.2.a.dc	$9350$	$2$	9350.a	1.a	$1$	$7$	$7$	$74.660$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1870.2.b.d	$1$	$1$	$7$	$-3$	$0$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
9350.2.a.dd	$9350$	$2$	9350.a	1.a	$1$	$13$	$13$	$74.660$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓		✓		1870.2.b.e	$1$	$0$	$-13$	$-3$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{11}q^{7}+\cdots$
9350.2.a.de	$9350$	$2$	9350.a	1.a	$1$	$13$	$13$	$74.660$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓		✓		1870.2.b.f	$1$	$0$	$-13$	$-1$	$0$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{4}q^{7}+\cdots$
9350.2.a.df	$9350$	$2$	9350.a	1.a	$1$	$13$	$13$	$74.660$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓		✓		1870.2.b.f	$1$	$0$	$13$	$1$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{4}q^{7}+\cdots$
9350.2.a.dg	$9350$	$2$	9350.a	1.a	$1$	$13$	$13$	$74.660$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓		✓		1870.2.b.e	$1$	$0$	$13$	$3$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{11}q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9350))$ 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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9350 = 2 \cdot 5^{2} \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9350.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 85 \)
Sturm bound:			\(3240\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\), \(19\)

\(2\)	\(5\)	\(11\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(5\)	\(11\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(93\)	\(15\)	\(78\)	\(91\)	\(15\)	\(76\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(111\)	\(16\)	\(95\)	\(108\)	\(16\)	\(92\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(108\)	\(16\)	\(92\)	\(105\)	\(16\)	\(89\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(96\)	\(13\)	\(83\)	\(93\)	\(13\)	\(80\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(109\)	\(19\)	\(90\)	\(106\)	\(19\)	\(87\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(98\)	\(15\)	\(83\)	\(95\)	\(15\)	\(80\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(101\)	\(13\)	\(88\)	\(98\)	\(13\)	\(85\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(106\)	\(21\)	\(85\)	\(103\)	\(21\)	\(82\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(105\)	\(16\)	\(89\)	\(102\)	\(16\)	\(86\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(102\)	\(12\)	\(90\)	\(99\)	\(12\)	\(87\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(99\)	\(13\)	\(86\)	\(96\)	\(13\)	\(83\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(108\)	\(19\)	\(89\)	\(105\)	\(19\)	\(86\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(104\)	\(15\)	\(89\)	\(101\)	\(15\)	\(86\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(100\)	\(21\)	\(79\)	\(97\)	\(21\)	\(76\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(103\)	\(21\)	\(82\)	\(100\)	\(21\)	\(79\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(101\)	\(11\)	\(90\)	\(98\)	\(11\)	\(87\)	\(3\)	\(0\)	\(3\)
Plus space				\(+\)	\(794\)	\(107\)	\(687\)	\(771\)	\(107\)	\(664\)	\(23\)	\(0\)	\(23\)
Minus space				\(-\)	\(850\)	\(149\)	\(701\)	\(826\)	\(149\)	\(677\)	\(24\)	\(0\)	\(24\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9350))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9350))\) 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	9350.2.a

Level	$9350$
Weight	$2$
Character orbit	9350.a
Rep. character	$\chi_{9350}(1,\cdot)$
Character field	$\Q$
Dimension	$256$
Newform subspaces	$85$
Sturm bound	$3240$
Trace bound	$11$