LMFDB - Space of modular forms of level 4650, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 68 $
Sturm bound:			$1920$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $11$, $13$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4650))$.

	Total	New	Old
Modular forms	984	94	890
Cusp forms	937	94	843
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.

$2$	$3$	$5$	$31$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$31$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$54$	$6$	$48$	$52$	$6$	$46$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$-$	$66$	$6$	$60$	$63$	$6$	$57$	$3$	$0$	$3$
$+$	$+$	$-$	$+$	$-$	$67$	$7$	$60$	$64$	$7$	$57$	$3$	$0$	$3$
$+$	$+$	$-$	$-$	$+$	$58$	$5$	$53$	$55$	$5$	$50$	$3$	$0$	$3$
$+$	$-$	$+$	$+$	$-$	$63$	$6$	$57$	$60$	$6$	$54$	$3$	$0$	$3$
$+$	$-$	$+$	$-$	$+$	$63$	$6$	$57$	$60$	$6$	$54$	$3$	$0$	$3$
$+$	$-$	$-$	$+$	$+$	$62$	$5$	$57$	$59$	$5$	$54$	$3$	$0$	$3$
$+$	$-$	$-$	$-$	$-$	$59$	$7$	$52$	$56$	$7$	$49$	$3$	$0$	$3$
$-$	$+$	$+$	$+$	$-$	$66$	$7$	$59$	$63$	$7$	$56$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$+$	$57$	$4$	$53$	$54$	$4$	$50$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$+$	$59$	$4$	$55$	$56$	$4$	$52$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$-$	$65$	$8$	$57$	$62$	$8$	$54$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$+$	$63$	$4$	$59$	$60$	$4$	$56$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$-$	$60$	$7$	$53$	$57$	$7$	$50$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$-$	$58$	$8$	$50$	$55$	$8$	$47$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$+$	$64$	$4$	$60$	$61$	$4$	$57$	$3$	$0$	$3$
Plus space				$+$	$480$	$38$	$442$	$457$	$38$	$419$	$23$	$0$	$23$
Minus space				$-$	$504$	$56$	$448$	$480$	$56$	$424$	$24$	$0$	$24$

Trace form

$ 94 q - 2 q^{2} + 94 q^{4} - 8 q^{7} - 2 q^{8} + 94 q^{9} - 16 q^{11} - 12 q^{13} - 8 q^{14} + 94 q^{16} - 4 q^{17} - 2 q^{18} - 12 q^{19} + 20 q^{26} - 8 q^{28} + 36 q^{29} - 2 q^{32} - 4 q^{33} + 36 q^{34}+ \cdots - 16 q^{99}+O(q^{100}) $

94 * q - 2 * q^2 + 94 * q^4 - 8 * q^7 - 2 * q^8 + 94 * q^9 - 16 * q^11 - 12 * q^13 - 8 * q^14 + 94 * q^16 - 4 * q^17 - 2 * q^18 - 12 * q^19 + 20 * q^26 - 8 * q^28 + 36 * q^29 - 2 * q^32 - 4 * q^33 + 36 * q^34 + 94 * q^36 + 12 * q^37 + 28 * q^41 + 8 * q^42 - 8 * q^43 - 16 * q^44 - 8 * q^46 + 24 * q^47 + 78 * q^49 - 20 * q^51 - 12 * q^52 - 20 * q^53 - 8 * q^56 - 16 * q^57 - 12 * q^58 - 24 * q^59 - 20 * q^61 - 8 * q^63 + 94 * q^64 - 8 * q^66 - 12 * q^67 - 4 * q^68 - 16 * q^69 + 8 * q^71 - 2 * q^72 - 12 * q^73 - 12 * q^74 - 12 * q^76 + 48 * q^77 - 12 * q^78 - 8 * q^79 + 94 * q^81 + 4 * q^82 + 48 * q^83 + 8 * q^87 + 20 * q^89 - 40 * q^91 + 2 * q^93 - 28 * q^94 + 16 * q^97 - 18 * q^98 - 16 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4650))$ 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	31	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4650.2.a.a	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.a	$1$	$1$	$-1$	$-1$	$0$	$-5$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots$
4650.2.a.b	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.b	$1$	$1$	$-1$	$-1$	$0$	$-3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
4650.2.a.c	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.e	$1$	$0$	$-1$	$-1$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
4650.2.a.d	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.n	$1$	$0$	$-1$	$-1$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
4650.2.a.e	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
4650.2.a.f	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.b	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
4650.2.a.g	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.g	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
4650.2.a.h	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.o	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
4650.2.a.i	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				186.2.a.c	$1$	$0$	$-1$	$-1$	$0$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
4650.2.a.j	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.f	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
4650.2.a.k	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.k	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
4650.2.a.l	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.l	$1$	$1$	$-1$	$-1$	$0$	$3$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots$
4650.2.a.m	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.c	$1$	$0$	$-1$	$-1$	$0$	$5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots$
4650.2.a.n	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.m	$1$	$0$	$-1$	$1$	$0$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
4650.2.a.o	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.o	$1$	$0$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
4650.2.a.p	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.a	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
4650.2.a.q	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.q	$1$	$0$	$-1$	$1$	$0$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
4650.2.a.r	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.l	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
4650.2.a.s	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.s	$1$	$0$	$-1$	$1$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
4650.2.a.t	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.k	$1$	$0$	$-1$	$1$	$0$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
4650.2.a.u	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.d	$1$	$1$	$-1$	$1$	$0$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
4650.2.a.v	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.v	$1$	$0$	$-1$	$1$	$0$	$3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
4650.2.a.w	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.g	$1$	$0$	$1$	$-1$	$0$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
4650.2.a.x	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.j	$1$	$1$	$1$	$-1$	$0$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
4650.2.a.y	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.v	$1$	$1$	$1$	$-1$	$0$	$-3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots$
4650.2.a.z	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.d	$1$	$1$	$1$	$-1$	$0$	$-2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
4650.2.a.ba	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.s	$1$	$1$	$1$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
4650.2.a.bb	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.f	$1$	$0$	$1$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
4650.2.a.bc	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.a	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.bd	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.i	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.be	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.o	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.bf	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.q	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.bg	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.h	$1$	$0$	$1$	$-1$	$0$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots$
4650.2.a.bh	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				186.2.a.b	$1$	$0$	$1$	$-1$	$0$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots$
4650.2.a.bi	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.c	$1$	$0$	$1$	$1$	$0$	$-5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots$
4650.2.a.bj	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.l	$1$	$0$	$1$	$1$	$0$	$-3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
4650.2.a.bk	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.e	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
4650.2.a.bl	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.d	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
4650.2.a.bm	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.f	$1$	$1$	$1$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
4650.2.a.bn	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.k	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
4650.2.a.bo	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				186.2.a.a	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
4650.2.a.bp	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.b	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
4650.2.a.bq	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.b	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.br	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.g	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
4650.2.a.bs	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.d.e	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
4650.2.a.bt	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.e	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
4650.2.a.bu	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.b	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
4650.2.a.bv	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.a	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
4650.2.a.bw	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓				930.2.a.c	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
4650.2.a.bx	$4650$	$2$	4650.a	1.a	$1$	$1$	$1$	$37.130$	$\Q$	None	✓	✓			4650.2.a.a	$1$	$0$	$1$	$1$	$0$	$5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+5q^{7}+q^{8}+\cdots$
4650.2.a.by	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{33}) $	None	✓		✓		930.2.a.r	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots$
4650.2.a.bz	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{65}) $	None	✓				930.2.a.q	$1$	$0$	$-2$	$-2$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots$
4650.2.a.ca	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{5}) $	None	✓	✓			4650.2.a.ca	$1$	$0$	$-2$	$-2$	$0$	$4$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots$
4650.2.a.cb	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{13}) $	None	✓	✓			4650.2.a.cb	$1$	$0$	$-2$	$-2$	$0$	$6$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots$
4650.2.a.cc	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{2}) $	None	✓				930.2.d.g	$1$	$0$	$-2$	$2$	$0$	$-4$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots$
4650.2.a.cd	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{17}) $	None	✓		✓		186.2.a.d	$1$	$0$	$-2$	$2$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2\beta q^{7}-q^{8}+\cdots$
4650.2.a.ce	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{17}) $	None	✓				930.2.a.p	$1$	$1$	$-2$	$2$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots$
4650.2.a.cf	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{2}) $	None	✓				930.2.d.g	$1$	$0$	$2$	$-2$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots$
4650.2.a.cg	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{13}) $	None	✓	✓	✓		4650.2.a.cb	$1$	$1$	$2$	$2$	$0$	$-6$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
4650.2.a.ch	$4650$	$2$	4650.a	1.a	$1$	$2$	$2$	$37.130$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4650.2.a.ca	$1$	$1$	$2$	$2$	$0$	$-4$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(-2-\beta )q^{7}+\cdots$
4650.2.a.ci	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1708.1	None	✓		✓		930.2.d.i	$1$	$0$	$-3$	$-3$	$0$	$-6$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
4650.2.a.cj	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.837.1	None	✓	✓	✓		4650.2.a.cj	$1$	$1$	$-3$	$3$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{2}q^{7}-q^{8}+\cdots$
4650.2.a.ck	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.940.1	None	✓		✓		930.2.d.h	$1$	$0$	$-3$	$3$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
4650.2.a.cl	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1373.1	None	✓	✓	✓		4650.2.a.cl	$1$	$1$	$-3$	$3$	$0$	$2$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1-\beta _{2})q^{7}+\cdots$
4650.2.a.cm	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1373.1	None	✓	✓			4650.2.a.cl	$1$	$0$	$3$	$-3$	$0$	$-2$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{2})q^{7}+\cdots$
4650.2.a.cn	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.940.1	None	✓				930.2.d.h	$1$	$0$	$3$	$-3$	$0$	$-1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
4650.2.a.co	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.837.1	None	✓	✓	✓		4650.2.a.cj	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{2}q^{7}+q^{8}+\cdots$
4650.2.a.cp	$4650$	$2$	4650.a	1.a	$1$	$3$	$3$	$37.130$	3.3.1708.1	None	✓		✓		930.2.d.i	$1$	$0$	$3$	$3$	$0$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4650))$ 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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 68 \)
Sturm bound:			\(1920\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

\(2\)	\(3\)	\(5\)	\(31\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(31\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(54\)	\(6\)	\(48\)	\(52\)	\(6\)	\(46\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(66\)	\(6\)	\(60\)	\(63\)	\(6\)	\(57\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(67\)	\(7\)	\(60\)	\(64\)	\(7\)	\(57\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(58\)	\(5\)	\(53\)	\(55\)	\(5\)	\(50\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(63\)	\(6\)	\(57\)	\(60\)	\(6\)	\(54\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(63\)	\(6\)	\(57\)	\(60\)	\(6\)	\(54\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(62\)	\(5\)	\(57\)	\(59\)	\(5\)	\(54\)	\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(59\)	\(7\)	\(52\)	\(56\)	\(7\)	\(49\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(66\)	\(7\)	\(59\)	\(63\)	\(7\)	\(56\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(57\)	\(4\)	\(53\)	\(54\)	\(4\)	\(50\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(59\)	\(4\)	\(55\)	\(56\)	\(4\)	\(52\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(65\)	\(8\)	\(57\)	\(62\)	\(8\)	\(54\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(63\)	\(4\)	\(59\)	\(60\)	\(4\)	\(56\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(60\)	\(7\)	\(53\)	\(57\)	\(7\)	\(50\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(58\)	\(8\)	\(50\)	\(55\)	\(8\)	\(47\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(64\)	\(4\)	\(60\)	\(61\)	\(4\)	\(57\)	\(3\)	\(0\)	\(3\)
Plus space				\(+\)	\(480\)	\(38\)	\(442\)	\(457\)	\(38\)	\(419\)	\(23\)	\(0\)	\(23\)
Minus space				\(-\)	\(504\)	\(56\)	\(448\)	\(480\)	\(56\)	\(424\)	\(24\)	\(0\)	\(24\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4650))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4650))\) 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	4650.2.a

Level	$4650$
Weight	$2$
Character orbit	4650.a
Rep. character	$\chi_{4650}(1,\cdot)$
Character field	$\Q$
Dimension	$94$
Newform subspaces	$68$
Sturm bound	$1920$
Trace bound	$13$