LMFDB - Space of modular forms of level 4830, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 57 $
Sturm bound:			$2304$
Trace bound:			$17$
Distinguishing $T_p$:			$11$, $13$, $17$, $19$, $29$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4830))$.

	Total	New	Old
Modular forms	1168	87	1081
Cusp forms	1137	87	1050
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.

$2$	$3$	$5$	$7$	$23$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$7$	$23$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$28$	$1$	$27$	$28$	$1$	$27$	$0$	$0$	$0$
$+$	$+$	$+$	$+$	$-$	$-$	$43$	$4$	$39$	$42$	$4$	$38$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$+$	$-$	$41$	$5$	$36$	$40$	$5$	$35$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$-$	$+$	$33$	$1$	$32$	$32$	$1$	$31$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$+$	$-$	$39$	$3$	$36$	$38$	$3$	$35$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$-$	$+$	$33$	$3$	$30$	$32$	$3$	$29$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$+$	$+$	$36$	$2$	$34$	$35$	$2$	$33$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$-$	$-$	$39$	$3$	$36$	$38$	$3$	$35$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$+$	$-$	$37$	$2$	$35$	$36$	$2$	$34$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$-$	$+$	$35$	$3$	$32$	$34$	$3$	$31$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$+$	$+$	$34$	$3$	$31$	$33$	$3$	$30$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$-$	$-$	$39$	$3$	$36$	$38$	$3$	$35$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$+$	$+$	$36$	$3$	$33$	$35$	$3$	$32$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$-$	$-$	$37$	$3$	$34$	$36$	$3$	$33$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$+$	$-$	$41$	$3$	$38$	$40$	$3$	$37$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$-$	$+$	$33$	$2$	$31$	$32$	$2$	$30$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$+$	$-$	$36$	$2$	$34$	$35$	$2$	$33$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$-$	$+$	$37$	$3$	$34$	$36$	$3$	$33$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$+$	$+$	$38$	$2$	$36$	$37$	$2$	$35$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$-$	$-$	$34$	$4$	$30$	$33$	$4$	$29$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$+$	$+$	$36$	$4$	$32$	$35$	$4$	$31$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$-$	$-$	$38$	$2$	$36$	$37$	$2$	$35$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$+$	$-$	$34$	$3$	$31$	$33$	$3$	$30$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$-$	$+$	$39$	$2$	$37$	$38$	$2$	$36$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$+$	$+$	$40$	$4$	$36$	$39$	$4$	$35$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$-$	$-$	$34$	$3$	$31$	$33$	$3$	$30$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$+$	$-$	$36$	$3$	$33$	$35$	$3$	$32$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$-$	$+$	$35$	$1$	$34$	$34$	$1$	$33$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$+$	$-$	$32$	$3$	$29$	$31$	$3$	$28$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$-$	$+$	$43$	$1$	$42$	$42$	$1$	$41$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$+$	$+$	$40$	$1$	$39$	$39$	$1$	$38$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$-$	$-$	$32$	$5$	$27$	$31$	$5$	$26$	$1$	$0$	$1$
Plus space					$+$	$576$	$36$	$540$	$561$	$36$	$525$	$15$	$0$	$15$
Minus space					$-$	$592$	$51$	$541$	$576$	$51$	$525$	$16$	$0$	$16$

Trace form

$ 87 q - q^{2} - q^{3} + 87 q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 87 q^{9} - q^{10} - 12 q^{11} - q^{12} - 14 q^{13} - q^{14} - q^{15} + 87 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - q^{20} - q^{21}+ \cdots - 12 q^{99}+O(q^{100}) $

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

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4830))$ 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	7	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4830.2.a.a	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓	✓	✓	4830.2.a.a	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.b	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.c	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.c	$1$	$0$	$-1$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.d	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓	✓	✓	4830.2.a.d	$1$	$1$	$-1$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.e	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.e	$1$	$0$	$-1$	$-1$	$1$	$-1$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.f	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.f	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.g	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.g	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.h	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.h	$1$	$0$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.i	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.i	$1$	$1$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.j	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.j	$1$	$0$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.k	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.k	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.l	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.l	$1$	$0$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.m	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.m	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.n	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.n	$1$	$0$	$-1$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.o	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.o	$1$	$1$	$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.p	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.p	$1$	$0$	$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.q	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.q	$1$	$1$	$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.r	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.r	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.s	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.s	$1$	$1$	$1$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.t	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.t	$1$	$1$	$1$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.u	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.u	$1$	$0$	$1$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.v	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.v	$1$	$1$	$1$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.w	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.w	$1$	$0$	$1$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.x	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.x	$1$	$0$	$1$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.y	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.y	$1$	$1$	$1$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.z	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.z	$1$	$1$	$1$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.ba	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.ba	$1$	$1$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bb	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bb	$1$	$0$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bc	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓	✓	✓	4830.2.a.bc	$1$	$1$	$1$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bd	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bd	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.be	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.be	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bf	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bf	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bg	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓	✓	✓	4830.2.a.bg	$1$	$1$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bh	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bh	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bi	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bi	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bj	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bj	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bk	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓	✓	✓	4830.2.a.bk	$1$	$1$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bl	$4830$	$2$	4830.a	1.a	$1$	$1$	$1$	$38.568$	$\Q$	None	✓	✓			4830.2.a.bl	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bm	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{33}) $	None	✓	✓	✓		4830.2.a.bm	$1$	$0$	$-2$	$-2$	$2$	$-2$	$+$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bn	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{13}) $	None	✓	✓	✓		4830.2.a.bn	$1$	$1$	$-2$	$2$	$-2$	$-2$	$+$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.bo	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{13}) $	None	✓	✓	✓		4830.2.a.bo	$1$	$1$	$-2$	$2$	$-2$	$2$	$+$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.bp	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{17}) $	None	✓	✓	✓		4830.2.a.bp	$1$	$0$	$-2$	$2$	$-2$	$2$	$+$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.bq	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4830.2.a.bq	$1$	$0$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.br	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{17}) $	None	✓	✓	✓		4830.2.a.br	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.bs	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4830.2.a.bs	$1$	$0$	$-2$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.bt	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	4830.2.a.bt	$1$	$0$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.bu	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4830.2.a.bu	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.bv	$4830$	$2$	4830.a	1.a	$1$	$2$	$2$	$38.568$	$\Q(\sqrt{33}) $	None	✓	✓	✓		4830.2.a.bv	$1$	$0$	$2$	$2$	$-2$	$-2$	$-$	$-$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bw	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	3.3.316.1	None	✓	✓	✓		4830.2.a.bw	$1$	$0$	$-3$	$-3$	$-3$	$-3$	$+$	$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.bx	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	$\Q(\zeta_{14})^+$	None	✓	✓	✓	✓	4830.2.a.bx	$1$	$1$	$-3$	$-3$	$3$	$-3$	$+$	$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.by	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	3.3.148.1	None	✓	✓	✓	✓	4830.2.a.by	$1$	$0$	$-3$	$-3$	$3$	$3$	$+$	$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.bz	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	3.3.148.1	None	✓	✓	✓		4830.2.a.bz	$1$	$0$	$3$	$-3$	$-3$	$3$	$-$	$+$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.ca	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	3.3.316.1	None	✓	✓	✓		4830.2.a.ca	$1$	$1$	$3$	$-3$	$3$	$-3$	$-$	$+$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
4830.2.a.cb	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	3.3.229.1	None	✓	✓	✓	✓	4830.2.a.cb	$1$	$0$	$3$	$-3$	$3$	$3$	$-$	$+$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4830.2.a.cc	$4830$	$2$	4830.a	1.a	$1$	$3$	$3$	$38.568$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		4830.2.a.cc	$1$	$1$	$3$	$3$	$-3$	$-3$	$-$	$-$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
4830.2.a.cd	$4830$	$2$	4830.a	1.a	$1$	$4$	$4$	$38.568$	4.4.10273.1	None	✓	✓	✓		4830.2.a.cd	$1$	$0$	$-4$	$-4$	$-4$	$4$	$+$	$+$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
4830.2.a.ce	$4830$	$2$	4830.a	1.a	$1$	$4$	$4$	$38.568$	4.4.6809.1	None	✓	✓	✓		4830.2.a.ce	$1$	$0$	$4$	$4$	$4$	$4$	$-$	$-$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4830))$ 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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 57 \)
Sturm bound:			\(2304\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(29\)

\(2\)	\(3\)	\(5\)	\(7\)	\(23\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(7\)	\(23\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(28\)	\(1\)	\(27\)	\(28\)	\(1\)	\(27\)	\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(43\)	\(4\)	\(39\)	\(42\)	\(4\)	\(38\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(41\)	\(5\)	\(36\)	\(40\)	\(5\)	\(35\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(33\)	\(1\)	\(32\)	\(32\)	\(1\)	\(31\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(39\)	\(3\)	\(36\)	\(38\)	\(3\)	\(35\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(33\)	\(3\)	\(30\)	\(32\)	\(3\)	\(29\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(36\)	\(2\)	\(34\)	\(35\)	\(2\)	\(33\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(39\)	\(3\)	\(36\)	\(38\)	\(3\)	\(35\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(37\)	\(2\)	\(35\)	\(36\)	\(2\)	\(34\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(35\)	\(3\)	\(32\)	\(34\)	\(3\)	\(31\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(34\)	\(3\)	\(31\)	\(33\)	\(3\)	\(30\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(39\)	\(3\)	\(36\)	\(38\)	\(3\)	\(35\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(36\)	\(3\)	\(33\)	\(35\)	\(3\)	\(32\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(37\)	\(3\)	\(34\)	\(36\)	\(3\)	\(33\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(41\)	\(3\)	\(38\)	\(40\)	\(3\)	\(37\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(33\)	\(2\)	\(31\)	\(32\)	\(2\)	\(30\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(36\)	\(2\)	\(34\)	\(35\)	\(2\)	\(33\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(37\)	\(3\)	\(34\)	\(36\)	\(3\)	\(33\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(38\)	\(2\)	\(36\)	\(37\)	\(2\)	\(35\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(34\)	\(4\)	\(30\)	\(33\)	\(4\)	\(29\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(36\)	\(4\)	\(32\)	\(35\)	\(4\)	\(31\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(38\)	\(2\)	\(36\)	\(37\)	\(2\)	\(35\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(34\)	\(3\)	\(31\)	\(33\)	\(3\)	\(30\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(39\)	\(2\)	\(37\)	\(38\)	\(2\)	\(36\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(40\)	\(4\)	\(36\)	\(39\)	\(4\)	\(35\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(34\)	\(3\)	\(31\)	\(33\)	\(3\)	\(30\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(36\)	\(3\)	\(33\)	\(35\)	\(3\)	\(32\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(35\)	\(1\)	\(34\)	\(34\)	\(1\)	\(33\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(32\)	\(3\)	\(29\)	\(31\)	\(3\)	\(28\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(43\)	\(1\)	\(42\)	\(42\)	\(1\)	\(41\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(40\)	\(1\)	\(39\)	\(39\)	\(1\)	\(38\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(32\)	\(5\)	\(27\)	\(31\)	\(5\)	\(26\)	\(1\)	\(0\)	\(1\)
Plus space					\(+\)	\(576\)	\(36\)	\(540\)	\(561\)	\(36\)	\(525\)	\(15\)	\(0\)	\(15\)
Minus space					\(-\)	\(592\)	\(51\)	\(541\)	\(576\)	\(51\)	\(525\)	\(16\)	\(0\)	\(16\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4830))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4830))\) 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	4830.2.a

Level	$4830$
Weight	$2$
Character orbit	4830.a
Rep. character	$\chi_{4830}(1,\cdot)$
Character field	$\Q$
Dimension	$87$
Newform subspaces	$57$
Sturm bound	$2304$
Trace bound	$17$