LMFDB - Space of modular forms of level 5850, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5850.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 72 $
Sturm bound:			$2520$
Trace bound:			$17$
Distinguishing $T_p$:			$7$, $11$, $17$, $23$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5850))$.

	Total	New	Old
Modular forms	1308	95	1213
Cusp forms	1213	95	1118
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.

$2$	$3$	$5$	$13$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$13$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$75$	$6$	$69$	$70$	$6$	$64$	$5$	$0$	$5$
$+$	$+$	$+$	$-$	$-$	$87$	$3$	$84$	$81$	$3$	$78$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$-$	$85$	$4$	$81$	$79$	$4$	$75$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$+$	$79$	$6$	$73$	$73$	$6$	$67$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$-$	$84$	$6$	$78$	$78$	$6$	$72$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$+$	$81$	$6$	$75$	$75$	$6$	$69$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$+$	$80$	$7$	$73$	$74$	$7$	$67$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$-$	$83$	$9$	$74$	$77$	$9$	$68$	$6$	$0$	$6$
$-$	$+$	$+$	$+$	$-$	$84$	$6$	$78$	$78$	$6$	$72$	$6$	$0$	$6$
$-$	$+$	$+$	$-$	$+$	$78$	$3$	$75$	$72$	$3$	$69$	$6$	$0$	$6$
$-$	$+$	$-$	$+$	$+$	$82$	$4$	$78$	$76$	$4$	$72$	$6$	$0$	$6$
$-$	$+$	$-$	$-$	$-$	$82$	$6$	$76$	$76$	$6$	$70$	$6$	$0$	$6$
$-$	$-$	$+$	$+$	$+$	$84$	$6$	$78$	$78$	$6$	$72$	$6$	$0$	$6$
$-$	$-$	$+$	$-$	$-$	$81$	$9$	$72$	$75$	$9$	$66$	$6$	$0$	$6$
$-$	$-$	$-$	$+$	$-$	$80$	$9$	$71$	$74$	$9$	$65$	$6$	$0$	$6$
$-$	$-$	$-$	$-$	$+$	$83$	$5$	$78$	$77$	$5$	$72$	$6$	$0$	$6$
Plus space				$+$	$642$	$43$	$599$	$595$	$43$	$552$	$47$	$0$	$47$
Minus space				$-$	$666$	$52$	$614$	$618$	$52$	$566$	$48$	$0$	$48$

Trace form

$ 95 q + q^{2} + 95 q^{4} + q^{8} + 4 q^{11} - q^{13} - 6 q^{14} + 95 q^{16} - 12 q^{17} - 8 q^{19} - 20 q^{22} + 12 q^{23} - 3 q^{26} + 2 q^{29} + 24 q^{31} + q^{32} + 6 q^{34} + 14 q^{37} + 4 q^{38}+ \cdots - 23 q^{98}+O(q^{100}) $

95 * q + q^2 + 95 * q^4 + q^8 + 4 * q^11 - q^13 - 6 * q^14 + 95 * q^16 - 12 * q^17 - 8 * q^19 - 20 * q^22 + 12 * q^23 - 3 * q^26 + 2 * q^29 + 24 * q^31 + q^32 + 6 * q^34 + 14 * q^37 + 4 * q^38 + 2 * q^41 + 14 * q^43 + 4 * q^44 + 4 * q^46 - 8 * q^47 + 105 * q^49 - q^52 - 2 * q^53 - 6 * q^56 + 22 * q^58 + 36 * q^59 + 2 * q^61 - 8 * q^62 + 95 * q^64 - 16 * q^67 - 12 * q^68 + 80 * q^71 - 10 * q^73 - 12 * q^74 - 8 * q^76 - 24 * q^77 - 4 * q^79 + 14 * q^82 + 24 * q^83 + 24 * q^86 - 20 * q^88 + 34 * q^89 - 6 * q^91 + 12 * q^92 + 26 * q^94 + 2 * q^97 - 23 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5850))$ 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	3	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5850.2.a.a	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.e	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{11}+q^{13}+\cdots$
5850.2.a.b	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.e	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-q^{11}-q^{13}+\cdots$
5850.2.a.c	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.c	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{13}+4q^{14}+\cdots$
5850.2.a.d	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				78.2.a.a	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+4q^{11}-q^{13}+\cdots$
5850.2.a.e	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.d	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+6q^{11}+q^{13}+\cdots$
5850.2.a.f	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.f	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}+q^{13}+\cdots$
5850.2.a.g	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.d	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{13}+2q^{14}+\cdots$
5850.2.a.h	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1170.2.a.f	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{11}+q^{13}+\cdots$
5850.2.a.i	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.i	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}-q^{13}+\cdots$
5850.2.a.j	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.m	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
5850.2.a.k	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.l	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+5q^{11}-q^{13}+\cdots$
5850.2.a.l	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.j	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-4q^{11}+q^{13}+q^{16}+\cdots$
5850.2.a.m	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.a	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+q^{13}+q^{16}-6q^{17}+\cdots$
5850.2.a.n	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.a	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+3q^{11}+q^{13}+q^{16}+\cdots$
5850.2.a.o	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.a	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+6q^{11}+q^{13}+q^{16}+\cdots$
5850.2.a.p	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				26.2.a.a	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}-q^{13}+\cdots$
5850.2.a.q	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.b	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}-q^{13}+\cdots$
5850.2.a.r	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.i	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-6q^{11}+q^{13}+\cdots$
5850.2.a.s	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.b	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}+q^{13}+\cdots$
5850.2.a.t	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.c	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-2q^{11}-q^{13}+\cdots$
5850.2.a.u	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.f	$1$	$0$	$-1$	$0$	$0$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-q^{13}+\cdots$
5850.2.a.v	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				234.2.a.a	$1$	$0$	$-1$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+4q^{11}+q^{13}+\cdots$
5850.2.a.w	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.a	$1$	$1$	$-1$	$0$	$0$	$3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
5850.2.a.x	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.b	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{11}+q^{13}+\cdots$
5850.2.a.y	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.f	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-q^{13}-4q^{14}+\cdots$
5850.2.a.z	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1170.2.a.c	$1$	$1$	$-1$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-q^{13}-4q^{14}+\cdots$
5850.2.a.ba	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				130.2.a.a	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+6q^{11}-q^{13}+\cdots$
5850.2.a.bb	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.f	$1$	$0$	$-1$	$0$	$0$	$5$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+5q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
5850.2.a.bc	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.f	$1$	$1$	$1$	$0$	$0$	$-5$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-5q^{7}+q^{8}+3q^{11}-q^{13}+\cdots$
5850.2.a.bd	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.b	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}-2q^{11}-q^{13}+\cdots$
5850.2.a.be	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.f	$1$	$1$	$1$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{13}-4q^{14}+\cdots$
5850.2.a.bf	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.a	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{7}+q^{8}+3q^{11}-q^{13}+\cdots$
5850.2.a.bg	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.i	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}-q^{13}+\cdots$
5850.2.a.bh	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1170.2.a.f	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-4q^{11}+q^{13}+\cdots$
5850.2.a.bi	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.e	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-4q^{11}+q^{13}+\cdots$
5850.2.a.bj	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.c	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-2q^{11}+q^{13}+\cdots$
5850.2.a.bk	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.g	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{13}-2q^{14}+\cdots$
5850.2.a.bl	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.f	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{11}+q^{13}+\cdots$
5850.2.a.bm	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.b	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
5850.2.a.bn	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				26.2.a.b	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+q^{13}+\cdots$
5850.2.a.bo	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.a.f	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-4q^{11}-q^{13}+q^{16}+\cdots$
5850.2.a.bp	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.j	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-4q^{11}-q^{13}+q^{16}+\cdots$
5850.2.a.bq	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				130.2.a.b	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+2q^{17}+\cdots$
5850.2.a.br	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.a	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+3q^{11}-q^{13}+q^{16}+\cdots$
5850.2.a.bs	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+6q^{11}-q^{13}+q^{16}+\cdots$
5850.2.a.bt	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.m	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}-q^{13}+\cdots$
5850.2.a.bu	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.l	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+q^{13}+\cdots$
5850.2.a.bv	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				234.2.a.a	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-4q^{11}+q^{13}+\cdots$
5850.2.a.bw	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.f	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}-q^{13}+\cdots$
5850.2.a.bx	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓	✓			5850.2.a.i	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+6q^{11}+q^{13}+\cdots$
5850.2.a.by	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1950.2.a.e	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}-4q^{11}-q^{13}+\cdots$
5850.2.a.bz	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				650.2.a.e	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}-q^{11}+q^{13}+\cdots$
5850.2.a.ca	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				1170.2.a.c	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}-q^{13}+4q^{14}+\cdots$
5850.2.a.cb	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				130.2.a.c	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}+q^{13}+\cdots$
5850.2.a.cc	$5850$	$2$	5850.a	1.a	$1$	$1$	$1$	$46.712$	$\Q$	None	✓				390.2.e.d	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+6q^{11}-q^{13}+\cdots$
5850.2.a.cd	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{7}) $	None	✓	✓			5850.2.a.cd	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}+3q^{11}+\cdots$
5850.2.a.ce	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{13}) $	None	✓				1170.2.a.p	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}-q^{13}+\cdots$
5850.2.a.cf	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{5}) $	None	✓				390.2.e.e	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}-2\beta q^{11}+\cdots$
5850.2.a.cg	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{41}) $	None	✓				1950.2.a.bc	$1$	$1$	$-2$	$0$	$0$	$3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots$
5850.2.a.ch	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{7}) $	None	✓	✓			5850.2.a.cd	$1$	$1$	$-2$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}-3q^{11}+\cdots$
5850.2.a.ci	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{7}) $	None	✓	✓			5850.2.a.cd	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}-3q^{11}+\cdots$
5850.2.a.cj	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{41}) $	None	✓				1950.2.a.bc	$1$	$0$	$2$	$0$	$0$	$-3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots$
5850.2.a.ck	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{13}) $	None	✓				1170.2.a.p	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-q^{13}+\cdots$
5850.2.a.cl	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{2}) $	None	✓				390.2.a.h	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{7}+q^{8}-2\beta q^{11}+\cdots$
5850.2.a.cm	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{5}) $	None	✓		✓		390.2.e.e	$1$	$1$	$2$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{7}+q^{8}-2\beta q^{11}+\cdots$
5850.2.a.cn	$5850$	$2$	5850.a	1.a	$1$	$2$	$2$	$46.712$	$\Q(\sqrt{7}) $	None	✓	✓			5850.2.a.cd	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta )q^{7}+q^{8}+3q^{11}+\cdots$
5850.2.a.co	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.148.1	None	✓		✓		1170.2.e.g	$1$	$0$	$-3$	$0$	$0$	$-4$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1})q^{7}-q^{8}+2q^{11}+\cdots$
5850.2.a.cp	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.940.1	None	✓		✓		130.2.b.a	$1$	$0$	$-3$	$0$	$0$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{7}-q^{8}+\cdots$
5850.2.a.cq	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.148.1	None	✓		✓		1170.2.e.g	$1$	$1$	$-3$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{7}-q^{8}-2q^{11}+\cdots$
5850.2.a.cr	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.148.1	None	✓		✓		1170.2.e.g	$1$	$1$	$3$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{7}+q^{8}-2q^{11}+\cdots$
5850.2.a.cs	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.940.1	None	✓		✓		130.2.b.a	$1$	$0$	$3$	$0$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{7}+q^{8}+\cdots$
5850.2.a.ct	$5850$	$2$	5850.a	1.a	$1$	$3$	$3$	$46.712$	3.3.148.1	None	✓		✓		1170.2.e.g	$1$	$0$	$3$	$0$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta _{1})q^{7}+q^{8}+2q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5850))$ 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:	\( N \)	\(=\)	\( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5850.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 72 \)
Sturm bound:			\(2520\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(23\), \(31\)

\(2\)	\(3\)	\(5\)	\(13\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(13\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(75\)	\(6\)	\(69\)	\(70\)	\(6\)	\(64\)	\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(87\)	\(3\)	\(84\)	\(81\)	\(3\)	\(78\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(85\)	\(4\)	\(81\)	\(79\)	\(4\)	\(75\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(79\)	\(6\)	\(73\)	\(73\)	\(6\)	\(67\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(84\)	\(6\)	\(78\)	\(78\)	\(6\)	\(72\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(81\)	\(6\)	\(75\)	\(75\)	\(6\)	\(69\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(80\)	\(7\)	\(73\)	\(74\)	\(7\)	\(67\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(83\)	\(9\)	\(74\)	\(77\)	\(9\)	\(68\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(84\)	\(6\)	\(78\)	\(78\)	\(6\)	\(72\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(78\)	\(3\)	\(75\)	\(72\)	\(3\)	\(69\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(82\)	\(4\)	\(78\)	\(76\)	\(4\)	\(72\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(82\)	\(6\)	\(76\)	\(76\)	\(6\)	\(70\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(84\)	\(6\)	\(78\)	\(78\)	\(6\)	\(72\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(81\)	\(9\)	\(72\)	\(75\)	\(9\)	\(66\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(80\)	\(9\)	\(71\)	\(74\)	\(9\)	\(65\)	\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(83\)	\(5\)	\(78\)	\(77\)	\(5\)	\(72\)	\(6\)	\(0\)	\(6\)
Plus space				\(+\)	\(642\)	\(43\)	\(599\)	\(595\)	\(43\)	\(552\)	\(47\)	\(0\)	\(47\)
Minus space				\(-\)	\(666\)	\(52\)	\(614\)	\(618\)	\(52\)	\(566\)	\(48\)	\(0\)	\(48\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5850))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5850))\) 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	5850.2.a

Level	$5850$
Weight	$2$
Character orbit	5850.a
Rep. character	$\chi_{5850}(1,\cdot)$
Character field	$\Q$
Dimension	$95$
Newform subspaces	$72$
Sturm bound	$2520$
Trace bound	$17$