LMFDB - Space of modular forms of level 1530, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 20 $
Sturm bound:			$648$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $11$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(1530))$.

	Total	New	Old
Modular forms	340	24	316
Cusp forms	309	24	285
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.

$2$	$3$	$5$	$17$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$2$
$+$	$+$	$+$	$-$	$-$	$1$
$+$	$+$	$-$	$-$	$+$	$1$
$+$	$-$	$+$	$+$	$-$	$3$
$+$	$-$	$+$	$-$	$+$	$1$
$+$	$-$	$-$	$+$	$+$	$2$
$+$	$-$	$-$	$-$	$-$	$2$
$-$	$+$	$+$	$+$	$-$	$1$
$-$	$+$	$-$	$+$	$+$	$1$
$-$	$+$	$-$	$-$	$-$	$2$
$-$	$-$	$+$	$+$	$+$	$2$
$-$	$-$	$+$	$-$	$-$	$3$
$-$	$-$	$-$	$+$	$-$	$3$
Plus space				$+$	$9$
Minus space				$-$	$15$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(1530))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	5	17	$q$-expansion
1530.2.a.a	$1$	$12.217$	$\Q$	None	$-1$	$0$	$-1$	$-4$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.b	$1$	$12.217$	$\Q$	None	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
1530.2.a.c	$1$	$12.217$	$\Q$	None	$-1$	$0$	$-1$	$2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.d	$1$	$12.217$	$\Q$	None	$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.e	$1$	$12.217$	$\Q$	None	$-1$	$0$	$1$	$-2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.f	$1$	$12.217$	$\Q$	None	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots$
1530.2.a.g	$1$	$12.217$	$\Q$	None	$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.h	$1$	$12.217$	$\Q$	None	$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.i	$1$	$12.217$	$\Q$	None	$1$	$0$	$-1$	$-2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.j	$1$	$12.217$	$\Q$	None	$1$	$0$	$-1$	$-2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.k	$1$	$12.217$	$\Q$	None	$1$	$0$	$-1$	$-2$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.l	$1$	$12.217$	$\Q$	None	$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.m	$1$	$12.217$	$\Q$	None	$1$	$0$	$1$	$-4$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.n	$1$	$12.217$	$\Q$	None	$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.o	$1$	$12.217$	$\Q$	None	$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.p	$1$	$12.217$	$\Q$	None	$1$	$0$	$1$	$2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.q	$2$	$12.217$	$\Q(\sqrt{5}) $	None	$-2$	$0$	$-2$	$2$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots$
1530.2.a.r	$2$	$12.217$	$\Q(\sqrt{17}) $	None	$-2$	$0$	$-2$	$2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.s	$2$	$12.217$	$\Q(\sqrt{6}) $	None	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.t	$2$	$12.217$	$\Q(\sqrt{5}) $	None	$2$	$0$	$2$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(1530))$ into lower level spaces

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Degree 3	Degree 4
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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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(648\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1530))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1530))\) 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	1530.2.a

Level	$1530$
Weight	$2$
Character orbit	1530.a
Rep. character	$\chi_{1530}(1,\cdot)$
Character field	$\Q$
Dimension	$24$
Newform subspaces	$20$
Sturm bound	$648$
Trace bound	$13$

\(2\)	\(3\)	\(5\)	\(17\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(3\)
Plus space				\(+\)	\(9\)
Minus space				\(-\)	\(15\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	5	17	$q$-expansion
1530.2.a.a	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.b	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
1530.2.a.c	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.d	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.e	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.f	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\)
1530.2.a.g	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.h	\(1\)	\(12.217\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.i	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.j	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.k	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.l	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.m	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-4\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.n	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.o	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.p	\(1\)	\(12.217\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.q	\(2\)	\(12.217\)	\(\Q(\sqrt{5}) \)	None	\(-2\)	\(0\)	\(-2\)	\(2\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
1530.2.a.r	\(2\)	\(12.217\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(0\)	\(-2\)	\(2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.s	\(2\)	\(12.217\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.t	\(2\)	\(12.217\)	\(\Q(\sqrt{5}) \)	None	\(2\)	\(0\)	\(2\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)