LMFDB - Space of modular forms of level 5610, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 63 $
Sturm bound:			$2592$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $13$, $19$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5610))$.

	Total	New	Old
Modular forms	1312	111	1201
Cusp forms	1281	111	1170
Eisenstein series	31	0	31

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

$2$	$3$	$5$	$11$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$11$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$30$	$5$	$25$	$30$	$5$	$25$	$0$	$0$	$0$
$+$	$+$	$+$	$+$	$-$	$-$	$49$	$2$	$47$	$48$	$2$	$46$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$+$	$-$	$47$	$2$	$45$	$46$	$2$	$44$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$-$	$+$	$37$	$4$	$33$	$36$	$4$	$32$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$+$	$-$	$45$	$3$	$42$	$44$	$3$	$41$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$-$	$+$	$38$	$4$	$34$	$37$	$4$	$33$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$+$	$+$	$39$	$2$	$37$	$38$	$2$	$36$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$-$	$-$	$43$	$4$	$39$	$42$	$4$	$38$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$+$	$-$	$40$	$4$	$36$	$39$	$4$	$35$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$-$	$+$	$42$	$4$	$38$	$41$	$4$	$37$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$+$	$+$	$47$	$3$	$44$	$46$	$3$	$43$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$-$	$-$	$36$	$4$	$32$	$35$	$4$	$31$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$+$	$+$	$42$	$4$	$38$	$41$	$4$	$37$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$-$	$-$	$42$	$4$	$38$	$41$	$4$	$37$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$+$	$-$	$38$	$5$	$33$	$37$	$5$	$32$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$-$	$+$	$41$	$2$	$39$	$40$	$2$	$38$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$+$	$-$	$38$	$3$	$35$	$37$	$3$	$34$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$-$	$+$	$47$	$2$	$45$	$46$	$2$	$44$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$+$	$+$	$40$	$3$	$37$	$39$	$3$	$36$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$-$	$-$	$40$	$5$	$35$	$39$	$5$	$34$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$+$	$+$	$46$	$3$	$43$	$45$	$3$	$42$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$-$	$-$	$35$	$4$	$31$	$34$	$4$	$30$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$+$	$-$	$37$	$5$	$32$	$36$	$5$	$31$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$-$	$+$	$45$	$1$	$44$	$44$	$1$	$43$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$+$	$+$	$42$	$3$	$39$	$41$	$3$	$38$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$-$	$-$	$40$	$5$	$35$	$39$	$5$	$34$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$+$	$-$	$44$	$5$	$39$	$43$	$5$	$38$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$-$	$+$	$37$	$2$	$35$	$36$	$2$	$34$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$+$	$-$	$45$	$5$	$40$	$44$	$5$	$39$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$-$	$+$	$35$	$1$	$34$	$34$	$1$	$33$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$+$	$+$	$36$	$1$	$35$	$35$	$1$	$34$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$-$	$-$	$49$	$7$	$42$	$48$	$7$	$41$	$1$	$0$	$1$
Plus space					$+$	$644$	$44$	$600$	$629$	$44$	$585$	$15$	$0$	$15$
Minus space					$-$	$668$	$67$	$601$	$652$	$67$	$585$	$16$	$0$	$16$

Trace form

$ 111 q - q^{2} + 7 q^{3} + 111 q^{4} - q^{5} - q^{6} + 8 q^{7} - q^{8} + 111 q^{9} - q^{10} - q^{11} + 7 q^{12} + 2 q^{13} - 8 q^{14} - q^{15} + 111 q^{16} - q^{17} - q^{18} - 4 q^{19} - q^{20}+ \cdots - q^{99}+O(q^{100}) $

111 * q - q^2 + 7 * q^3 + 111 * q^4 - q^5 - q^6 + 8 * q^7 - q^8 + 111 * q^9 - q^10 - q^11 + 7 * q^12 + 2 * q^13 - 8 * q^14 - q^15 + 111 * q^16 - q^17 - q^18 - 4 * q^19 - q^20 + 8 * q^21 + 7 * q^22 - 8 * q^23 - q^24 + 111 * q^25 + 2 * q^26 + 7 * q^27 + 8 * q^28 - 30 * q^29 - q^30 - q^32 - q^33 - q^34 - 8 * q^35 + 111 * q^36 + 26 * q^37 + 28 * q^38 + 34 * q^39 - q^40 + 22 * q^41 - 8 * q^42 + 36 * q^43 - q^44 - q^45 + 8 * q^46 + 16 * q^47 + 7 * q^48 + 119 * q^49 - q^50 - q^51 + 2 * q^52 + 26 * q^53 - q^54 - q^55 - 8 * q^56 + 28 * q^57 + 2 * q^58 + 20 * q^59 - q^60 + 18 * q^61 + 32 * q^62 + 8 * q^63 + 111 * q^64 + 18 * q^65 - q^66 + 60 * q^67 - q^68 + 8 * q^69 - 8 * q^70 + 8 * q^71 - q^72 + 6 * q^73 - 6 * q^74 + 7 * q^75 - 4 * q^76 + 8 * q^77 + 2 * q^78 + 64 * q^79 - q^80 + 111 * q^81 + 22 * q^82 + 44 * q^83 + 8 * q^84 - q^85 + 68 * q^86 + 34 * q^87 + 7 * q^88 - 26 * q^89 - q^90 - 16 * q^91 - 8 * q^92 + 16 * q^93 + 16 * q^94 - 20 * q^95 - q^96 + 30 * q^97 + 71 * q^98 - q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5610))$ 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	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5610.2.a.a	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
5610.2.a.b	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.b	$1$	$1$	$-1$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
5610.2.a.c	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.c	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
5610.2.a.d	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.d	$1$	$0$	$-1$	$-1$	$-1$	$1$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
5610.2.a.e	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.e	$1$	$1$	$-1$	$-1$	$-1$	$4$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
5610.2.a.f	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.f	$1$	$0$	$-1$	$-1$	$1$	$-3$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
5610.2.a.g	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.g	$1$	$0$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
5610.2.a.h	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.h	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
5610.2.a.i	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.i	$1$	$0$	$-1$	$-1$	$1$	$2$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
5610.2.a.j	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.j	$1$	$1$	$-1$	$-1$	$1$	$3$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
5610.2.a.k	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.k	$1$	$1$	$-1$	$1$	$-1$	$-3$	$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots$
5610.2.a.l	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.l	$1$	$1$	$-1$	$1$	$-1$	$-3$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots$
5610.2.a.m	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.m	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
5610.2.a.n	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.n	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
5610.2.a.o	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.o	$1$	$1$	$-1$	$1$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5610.2.a.p	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.p	$1$	$0$	$-1$	$1$	$-1$	$3$	$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots$
5610.2.a.q	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.q	$1$	$0$	$-1$	$1$	$1$	$-4$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
5610.2.a.r	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.r	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
5610.2.a.s	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.s	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
5610.2.a.t	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.t	$1$	$0$	$-1$	$1$	$1$	$2$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
5610.2.a.u	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.u	$1$	$1$	$-1$	$1$	$1$	$2$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
5610.2.a.v	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.v	$1$	$0$	$-1$	$1$	$1$	$4$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
5610.2.a.w	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.w	$1$	$1$	$1$	$-1$	$-1$	$-4$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
5610.2.a.x	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.x	$1$	$0$	$1$	$-1$	$-1$	$-2$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
5610.2.a.y	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.y	$1$	$0$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
5610.2.a.z	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.z	$1$	$0$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
5610.2.a.ba	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.ba	$1$	$0$	$1$	$-1$	$-1$	$4$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
5610.2.a.bb	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓	✓	✓	5610.2.a.bb	$1$	$1$	$1$	$-1$	$1$	$-2$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
5610.2.a.bc	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bc	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
5610.2.a.bd	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bd	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
5610.2.a.be	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.be	$1$	$1$	$1$	$1$	$-1$	$-4$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
5610.2.a.bf	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bf	$1$	$1$	$1$	$1$	$-1$	$-4$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
5610.2.a.bg	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bg	$1$	$0$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
5610.2.a.bh	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bh	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
5610.2.a.bi	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bi	$1$	$0$	$1$	$1$	$-1$	$4$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
5610.2.a.bj	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓			5610.2.a.bj	$1$	$0$	$1$	$1$	$-1$	$5$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+5q^{7}+\cdots$
5610.2.a.bk	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓	✓	✓	5610.2.a.bk	$1$	$1$	$1$	$1$	$1$	$-4$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
5610.2.a.bl	$5610$	$2$	5610.a	1.a	$1$	$1$	$1$	$44.796$	$\Q$	None	✓	✓	✓	✓	5610.2.a.bl	$1$	$1$	$1$	$1$	$1$	$-2$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
5610.2.a.bm	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{17}) $	None	✓	✓			5610.2.a.bm	$1$	$1$	$-2$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
5610.2.a.bn	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	5610.2.a.bn	$1$	$0$	$-2$	$-2$	$-2$	$-1$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots$
5610.2.a.bo	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{41}) $	None	✓	✓	✓		5610.2.a.bo	$1$	$1$	$-2$	$-2$	$-2$	$-1$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots$
5610.2.a.bp	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{33}) $	None	✓	✓			5610.2.a.bp	$1$	$1$	$-2$	$-2$	$-2$	$1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots$
5610.2.a.bq	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{33}) $	None	✓	✓			5610.2.a.bq	$1$	$0$	$-2$	$-2$	$2$	$-1$	$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta q^{7}+\cdots$
5610.2.a.br	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{5}) $	None	✓	✓			5610.2.a.br	$1$	$0$	$-2$	$-2$	$2$	$2$	$+$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
5610.2.a.bs	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{13}) $	None	✓	✓	✓		5610.2.a.bs	$1$	$1$	$-2$	$2$	$-2$	$2$	$+$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
5610.2.a.bt	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	5610.2.a.bt	$1$	$1$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
5610.2.a.bu	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{5}) $	None	✓	✓	✓		5610.2.a.bu	$1$	$1$	$2$	$-2$	$-2$	$2$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
5610.2.a.bv	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{41}) $	None	✓	✓	✓		5610.2.a.bv	$1$	$0$	$2$	$-2$	$2$	$-3$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5610.2.a.bw	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{17}) $	None	✓	✓	✓		5610.2.a.bw	$1$	$1$	$2$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
5610.2.a.bx	$5610$	$2$	5610.a	1.a	$1$	$2$	$2$	$44.796$	$\Q(\sqrt{33}) $	None	✓	✓			5610.2.a.bx	$1$	$0$	$2$	$2$	$2$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$
5610.2.a.by	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		5610.2.a.by	$1$	$0$	$-3$	$3$	$-3$	$0$	$+$	$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
5610.2.a.bz	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.148.1	None	✓	✓	✓		5610.2.a.bz	$1$	$1$	$-3$	$3$	$3$	$-4$	$+$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5610.2.a.ca	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.961.1	None	✓	✓	✓		5610.2.a.ca	$1$	$0$	$-3$	$3$	$3$	$1$	$+$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
5610.2.a.cb	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.2089.1	None	✓	✓	✓		5610.2.a.cb	$1$	$0$	$-3$	$3$	$3$	$3$	$+$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
5610.2.a.cc	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	$\Q(\zeta_{14})^+$	None	✓	✓	✓	✓	5610.2.a.cc	$1$	$1$	$3$	$-3$	$3$	$-2$	$-$	$+$	$-$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5610.2.a.cd	$5610$	$2$	5610.a	1.a	$1$	$3$	$3$	$44.796$	3.3.2089.1	None	✓	✓	✓		5610.2.a.cd	$1$	$0$	$3$	$3$	$-3$	$1$	$-$	$-$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots$
5610.2.a.ce	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.2777.1	None	✓	✓	✓	✓	5610.2.a.ce	$1$	$1$	$-4$	$-4$	$4$	$-1$	$+$	$+$	$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
5610.2.a.cf	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.17428.1	None	✓	✓	✓	✓	5610.2.a.cf	$1$	$0$	$-4$	$4$	$-4$	$5$	$+$	$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
5610.2.a.cg	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.54764.1	None	✓	✓	✓		5610.2.a.cg	$1$	$0$	$4$	$-4$	$-4$	$4$	$-$	$+$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
5610.2.a.ch	$5610$	$2$	5610.a	1.a	$1$	$4$	$4$	$44.796$	4.4.65905.1	None	✓	✓	✓		5610.2.a.ch	$1$	$0$	$4$	$4$	$-4$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots$
5610.2.a.ci	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.18569692.1	None	✓	✓	✓	✓	5610.2.a.ci	$1$	$0$	$5$	$-5$	$5$	$2$	$-$	$+$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-\beta _{3}q^{7}+\cdots$
5610.2.a.cj	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.1284160.1	None	✓	✓	✓		5610.2.a.cj	$1$	$0$	$5$	$5$	$5$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
5610.2.a.ck	$5610$	$2$	5610.a	1.a	$1$	$5$	$5$	$44.796$	5.5.19985813.1	None	✓	✓	✓	✓	5610.2.a.ck	$1$	$0$	$5$	$5$	$5$	$2$	$-$	$-$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{2}q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5610))$ 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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 63 \)
Sturm bound:			\(2592\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\), \(19\), \(23\)

\(2\)	\(3\)	\(5\)	\(11\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(11\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(30\)	\(5\)	\(25\)	\(30\)	\(5\)	\(25\)	\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(49\)	\(2\)	\(47\)	\(48\)	\(2\)	\(46\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(47\)	\(2\)	\(45\)	\(46\)	\(2\)	\(44\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(37\)	\(4\)	\(33\)	\(36\)	\(4\)	\(32\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(45\)	\(3\)	\(42\)	\(44\)	\(3\)	\(41\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(38\)	\(4\)	\(34\)	\(37\)	\(4\)	\(33\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(39\)	\(2\)	\(37\)	\(38\)	\(2\)	\(36\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(43\)	\(4\)	\(39\)	\(42\)	\(4\)	\(38\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(40\)	\(4\)	\(36\)	\(39\)	\(4\)	\(35\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(42\)	\(4\)	\(38\)	\(41\)	\(4\)	\(37\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(47\)	\(3\)	\(44\)	\(46\)	\(3\)	\(43\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(36\)	\(4\)	\(32\)	\(35\)	\(4\)	\(31\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(42\)	\(4\)	\(38\)	\(41\)	\(4\)	\(37\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(42\)	\(4\)	\(38\)	\(41\)	\(4\)	\(37\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(38\)	\(5\)	\(33\)	\(37\)	\(5\)	\(32\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(41\)	\(2\)	\(39\)	\(40\)	\(2\)	\(38\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(38\)	\(3\)	\(35\)	\(37\)	\(3\)	\(34\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(47\)	\(2\)	\(45\)	\(46\)	\(2\)	\(44\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(40\)	\(3\)	\(37\)	\(39\)	\(3\)	\(36\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(40\)	\(5\)	\(35\)	\(39\)	\(5\)	\(34\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(46\)	\(3\)	\(43\)	\(45\)	\(3\)	\(42\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(35\)	\(4\)	\(31\)	\(34\)	\(4\)	\(30\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(37\)	\(5\)	\(32\)	\(36\)	\(5\)	\(31\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(45\)	\(1\)	\(44\)	\(44\)	\(1\)	\(43\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(42\)	\(3\)	\(39\)	\(41\)	\(3\)	\(38\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(40\)	\(5\)	\(35\)	\(39\)	\(5\)	\(34\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(44\)	\(5\)	\(39\)	\(43\)	\(5\)	\(38\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(37\)	\(2\)	\(35\)	\(36\)	\(2\)	\(34\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(45\)	\(5\)	\(40\)	\(44\)	\(5\)	\(39\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(35\)	\(1\)	\(34\)	\(34\)	\(1\)	\(33\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(36\)	\(1\)	\(35\)	\(35\)	\(1\)	\(34\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(49\)	\(7\)	\(42\)	\(48\)	\(7\)	\(41\)	\(1\)	\(0\)	\(1\)
Plus space					\(+\)	\(644\)	\(44\)	\(600\)	\(629\)	\(44\)	\(585\)	\(15\)	\(0\)	\(15\)
Minus space					\(-\)	\(668\)	\(67\)	\(601\)	\(652\)	\(67\)	\(585\)	\(16\)	\(0\)	\(16\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5610))\) 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	5610.2.a

Level	$5610$
Weight	$2$
Character orbit	5610.a
Rep. character	$\chi_{5610}(1,\cdot)$
Character field	$\Q$
Dimension	$111$
Newform subspaces	$63$
Sturm bound	$2592$
Trace bound	$13$