LMFDB - Space of modular forms of level 2700, weight 3, and Character 2700.g

Defining parameters

Level:	$ N $	$=$	$ 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2700.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 3 $
Character field:			$\Q$
Newform subspaces:			$ 19 $
Sturm bound:			$1620$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $11$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(2700, [\chi])$.

	Total	New	Old
Modular forms	1134	51	1083
Cusp forms	1026	51	975
Eisenstein series	108	0	108

Trace form

Decomposition of $S_{3}^{\mathrm{new}}(2700, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2700.3.g.a	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-13$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-13q^{7}-22q^{13}+11q^{19}-13q^{31}+\cdots$
2700.3.g.b	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-11$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{7}-23q^{13}-37q^{19}-46q^{31}+\cdots$
2700.3.g.c	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-11$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{7}+22q^{13}-37q^{19}+59q^{31}+\cdots$
2700.3.g.d	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{7}-23q^{13}+26q^{19}-13q^{31}+\cdots$
2700.3.g.e	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{7}+23q^{13}+26q^{19}-13q^{31}+\cdots$
2700.3.g.f	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$11$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+11q^{7}-22q^{13}-37q^{19}+59q^{31}+\cdots$
2700.3.g.g	$2700$	$3$	2700.g	3.b	$2$	$1$	$1$	$73.570$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$13$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+13q^{7}+22q^{13}+11q^{19}-13q^{31}+\cdots$
2700.3.g.h	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$0$	$0$	$-16$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q-8q^{7}+3\beta q^{11}+13q^{13}+\beta q^{17}+\cdots$
2700.3.g.i	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$0$	$0$	$-2$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{7}-\beta q^{11}+2q^{13}-2\beta q^{17}-7q^{19}+\cdots$
2700.3.g.j	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$0$	$0$	$2$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{7}-\beta q^{11}-2q^{13}+2\beta q^{17}-7q^{19}+\cdots$
2700.3.g.k	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$0$	$0$	$8$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q+4q^{7}-\beta q^{11}+7q^{13}+3\beta q^{17}+\cdots$
2700.3.g.l	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$0$	$0$	$14$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+7q^{7}+\beta q^{11}-17q^{13}+2\beta q^{17}+\cdots$
2700.3.g.m	$2700$	$3$	2700.g	3.b	$2$	$2$	$2$	$73.570$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$14$	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+7q^{7}-iq^{11}-14q^{13}+2iq^{17}+\cdots$
2700.3.g.n	$2700$	$3$	2700.g	3.b	$2$	$4$	$4$	$73.570$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$-20$	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-5+\beta _{3})q^{7}+(\beta _{1}-\beta _{2})q^{11}+(7+\cdots)q^{13}+\cdots$
2700.3.g.o	$2700$	$3$	2700.g	3.b	$2$	$4$	$4$	$73.570$	4.0.9292960.2	None		$2$	$0$	$0$	$0$	$0$	$-6$	$5$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{3})q^{7}-\beta _{1}q^{11}-3q^{13}+\cdots$
2700.3.g.p	$2700$	$3$	2700.g	3.b	$2$	$4$	$4$	$73.570$	4.0.9292960.2	None		$2$	$0$	$0$	$0$	$0$	$6$	$5$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{3})q^{7}-\beta _{1}q^{11}+3q^{13}+\beta _{2}q^{17}+\cdots$
2700.3.g.q	$2700$	$3$	2700.g	3.b	$2$	$6$	$6$	$73.570$	6.0.125798656.1	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{7}+\beta _{4}q^{11}+(-1-\beta _{3})q^{13}+\cdots$
2700.3.g.r	$2700$	$3$	2700.g	3.b	$2$	$6$	$6$	$73.570$	6.0.125798656.1	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{7}-\beta _{4}q^{11}+(1+\beta _{3})q^{13}-\beta _{5}q^{17}+\cdots$
2700.3.g.s	$2700$	$3$	2700.g	3.b	$2$	$8$	$8$	$73.570$	8.0.$\cdots$.6	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{7}+(-\beta _{3}+\beta _{6})q^{11}+(\beta _{1}-\beta _{5}+\cdots)q^{13}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(2700, [\chi])$ into lower level spaces

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

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2700.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1620\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{3}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Decomposition of \(S_{3}^{\mathrm{old}}(2700, [\chi])\) 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	2700.3.g

Level	$2700$
Weight	$3$
Character orbit	2700.g
Rep. character	$\chi_{2700}(701,\cdot)$
Character field	$\Q$
Dimension	$51$
Newform subspaces	$19$
Sturm bound	$1620$
Trace bound	$13$