LMFDB - Space of modular forms of level 5077, weight 2, and Trivial character

Defining parameters

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 3 $
Sturm bound:			$846$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5077))$.

	Total	New
Modular forms	423	423
Cusp forms	422	422
Eisenstein series	1	1

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

$5077$	Dim.
$+$	$206$
$-$	$216$

Trace form

$ 422q - 2q^{2} + 420q^{4} - 2q^{5} + 6q^{6} - 4q^{7} + 426q^{9} + O(q^{10}) $

$ 422q - 2q^{2} + 420q^{4} - 2q^{5} + 6q^{6} - 4q^{7} + 426q^{9} + 4q^{10} - 6q^{13} - 6q^{14} + 10q^{15} + 412q^{16} - 12q^{18} - 22q^{20} + 2q^{21} - 2q^{22} + 6q^{23} + 16q^{24} + 418q^{25} - 12q^{26} - 10q^{28} + 2q^{29} + 12q^{30} - 2q^{31} - 12q^{32} + 24q^{33} + 8q^{34} - 18q^{35} + 440q^{36} - 10q^{37} - 26q^{38} + 4q^{39} - 2q^{40} + 2q^{41} + 10q^{42} + 2q^{43} - 6q^{44} - 4q^{45} - 28q^{46} + 8q^{48} + 402q^{49} - 10q^{50} + 6q^{51} - 30q^{52} + 4q^{53} + 46q^{54} + 4q^{55} - 72q^{56} + 6q^{57} - 8q^{59} + 10q^{60} - 6q^{61} - 48q^{62} - 30q^{63} + 424q^{64} - 8q^{65} - 54q^{66} + 2q^{67} + 14q^{68} + 34q^{69} - 4q^{70} - 18q^{71} + 24q^{72} - 14q^{73} - 16q^{74} - 52q^{75} + 4q^{76} + 6q^{77} + 72q^{78} - 28q^{79} - 42q^{80} + 470q^{81} - 16q^{82} - 32q^{83} - 16q^{84} - 38q^{85} - 32q^{86} - 18q^{87} - 18q^{89} - 60q^{90} - 46q^{91} - 10q^{92} + 10q^{93} + 28q^{94} - 26q^{95} - 12q^{97} - 24q^{98} + 28q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5077))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	5077	$q$-expansion
5077.2.a.a	$1$	$40.540$	$\Q$	None	$-2$	$-3$	$-4$	$-4$	$+$	$q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots$
5077.2.a.b	$205$	$40.540$		None	$-25$	$-59$	$-44$	$-30$	$+$
5077.2.a.c	$216$	$40.540$		None	$25$	$62$	$46$	$30$	$-$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	($ 1 + 2 T + 2 T^{2} $)
$3$	($ 1 + 3 T + 3 T^{2} $)
$5$	($ 1 + 4 T + 5 T^{2} $)
$7$	($ 1 + 4 T + 7 T^{2} $)
$11$	($ 1 + 6 T + 11 T^{2} $)
$13$	($ 1 + 4 T + 13 T^{2} $)
$17$	($ 1 + 4 T + 17 T^{2} $)
$19$	($ 1 + 7 T + 19 T^{2} $)
$23$	($ 1 + 6 T + 23 T^{2} $)
$29$	($ 1 + 6 T + 29 T^{2} $)
$31$	($ 1 + 2 T + 31 T^{2} $)
$37$	($ 1 + 37 T^{2} $)
$41$	($ 1 + 41 T^{2} $)
$43$	($ 1 + 8 T + 43 T^{2} $)
$47$	($ 1 + 9 T + 47 T^{2} $)
$53$	($ 1 + 9 T + 53 T^{2} $)
$59$	($ 1 + 11 T + 59 T^{2} $)
$61$	($ 1 + 2 T + 61 T^{2} $)
$67$	($ 1 + 12 T + 67 T^{2} $)
$71$	($ 1 + 8 T + 71 T^{2} $)
$73$	($ 1 + 14 T + 73 T^{2} $)
$79$	($ 1 - 9 T + 79 T^{2} $)
$83$	($ 1 + 2 T + 83 T^{2} $)
$89$	($ 1 - 11 T + 89 T^{2} $)
$97$	($ 1 - 6 T + 97 T^{2} $)
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Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(846\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5077))\) into newform subspaces

Hecke characteristic polynomials

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	5077.2.a

Level	5077
Weight	2
Character orbit	a
Rep. character	\(\chi_{5077}(1,\cdot)\)
Character field	\(\Q\)
Dimension	422
Newform subspaces	3
Sturm bound	846
Trace bound	1

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	5077	$q$-expansion
5077.2.a.a	\(1\)	\(40.540\)	\(\Q\)	None	\(-2\)	\(-3\)	\(-4\)	\(-4\)	\(+\)	\(q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots\)
5077.2.a.b	\(205\)	\(40.540\)		None	\(-25\)	\(-59\)	\(-44\)	\(-30\)	\(+\)
5077.2.a.c	\(216\)	\(40.540\)		None	\(25\)	\(62\)	\(46\)	\(30\)	\(-\)

$p$	$F_p(T)$
$2$	(\( 1 + 2 T + 2 T^{2} \))
$3$	(\( 1 + 3 T + 3 T^{2} \))
$5$	(\( 1 + 4 T + 5 T^{2} \))
$7$	(\( 1 + 4 T + 7 T^{2} \))
$11$	(\( 1 + 6 T + 11 T^{2} \))
$13$	(\( 1 + 4 T + 13 T^{2} \))
$17$	(\( 1 + 4 T + 17 T^{2} \))
$19$	(\( 1 + 7 T + 19 T^{2} \))
$23$	(\( 1 + 6 T + 23 T^{2} \))
$29$	(\( 1 + 6 T + 29 T^{2} \))
$31$	(\( 1 + 2 T + 31 T^{2} \))
$37$	(\( 1 + 37 T^{2} \))
$41$	(\( 1 + 41 T^{2} \))
$43$	(\( 1 + 8 T + 43 T^{2} \))
$47$	(\( 1 + 9 T + 47 T^{2} \))
$53$	(\( 1 + 9 T + 53 T^{2} \))
$59$	(\( 1 + 11 T + 59 T^{2} \))
$61$	(\( 1 + 2 T + 61 T^{2} \))
$67$	(\( 1 + 12 T + 67 T^{2} \))
$71$	(\( 1 + 8 T + 71 T^{2} \))
$73$	(\( 1 + 14 T + 73 T^{2} \))
$79$	(\( 1 - 9 T + 79 T^{2} \))
$83$	(\( 1 + 2 T + 83 T^{2} \))
$89$	(\( 1 - 11 T + 89 T^{2} \))
$97$	(\( 1 - 6 T + 97 T^{2} \))
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