LMFDB - Space of Modular Forms of Level 4020, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	4020.a (trivial)
Character field:			$\Q$
Newforms:			$ 9 $
Sturm bound:			$1632$
Trace bound:			$5$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4020))$.

	Total	New	Old
Modular forms	828	44	784
Cusp forms	805	44	761
Eisenstein series	23	0	23

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

$2$	$3$	$5$	$67$	Fricke	Dim.
$-$	$+$	$+$	$+$	$-$	$7$
$-$	$+$	$+$	$-$	$+$	$4$
$-$	$+$	$-$	$+$	$+$	$5$
$-$	$+$	$-$	$-$	$-$	$6$
$-$	$-$	$+$	$+$	$+$	$5$
$-$	$-$	$+$	$-$	$-$	$6$
$-$	$-$	$-$	$+$	$-$	$7$
$-$	$-$	$-$	$-$	$+$	$4$
Plus space				$+$	$18$
Minus space				$-$	$26$

Trace form

$44q $ $\mathstrut +\mathstrut 44q^{9} $ $\mathstrut +\mathstrut O(q^{10}) $

$44q $ $\mathstrut +\mathstrut 44q^{9} $ $\mathstrut -\mathstrut 8q^{11} $ $\mathstrut +\mathstrut 4q^{17} $ $\mathstrut -\mathstrut 4q^{19} $ $\mathstrut -\mathstrut 12q^{23} $ $\mathstrut +\mathstrut 44q^{25} $ $\mathstrut +\mathstrut 4q^{29} $ $\mathstrut -\mathstrut 8q^{31} $ $\mathstrut -\mathstrut 8q^{35} $ $\mathstrut -\mathstrut 12q^{37} $ $\mathstrut -\mathstrut 16q^{41} $ $\mathstrut +\mathstrut 16q^{43} $ $\mathstrut -\mathstrut 4q^{47} $ $\mathstrut +\mathstrut 20q^{49} $ $\mathstrut +\mathstrut 8q^{51} $ $\mathstrut -\mathstrut 8q^{53} $ $\mathstrut -\mathstrut 4q^{59} $ $\mathstrut +\mathstrut 16q^{61} $ $\mathstrut -\mathstrut 8q^{65} $ $\mathstrut -\mathstrut 4q^{67} $ $\mathstrut -\mathstrut 16q^{69} $ $\mathstrut +\mathstrut 8q^{71} $ $\mathstrut +\mathstrut 4q^{73} $ $\mathstrut +\mathstrut 16q^{77} $ $\mathstrut +\mathstrut 24q^{79} $ $\mathstrut +\mathstrut 44q^{81} $ $\mathstrut +\mathstrut 16q^{83} $ $\mathstrut +\mathstrut 8q^{87} $ $\mathstrut -\mathstrut 28q^{89} $ $\mathstrut -\mathstrut 24q^{91} $ $\mathstrut -\mathstrut 8q^{93} $ $\mathstrut -\mathstrut 16q^{97} $ $\mathstrut -\mathstrut 8q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4020))$ into irreducible Hecke orbits

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	67	$q$-expansion
4020.2.a.a	$1$	$32.100$	$\Q$	None	$0$	$1$	$-1$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
4020.2.a.b	$4$	$32.100$	4.4.9301.1	None	$0$	$-4$	$-4$	$-1$	$-$	$+$	$+$	$-$	$q-q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4020.2.a.c	$4$	$32.100$	4.4.98117.1	None	$0$	$4$	$-4$	$1$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$
4020.2.a.d	$4$	$32.100$	$\Q(\zeta_{15})^+$	None	$0$	$4$	$4$	$-3$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots$
4020.2.a.e	$5$	$32.100$	5.5.1257629.1	None	$0$	$-5$	$5$	$-3$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
4020.2.a.f	$6$	$32.100$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$0$	$-6$	$6$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{5})q^{11}+\cdots$
4020.2.a.g	$6$	$32.100$	6.6.195727752.1	None	$0$	$6$	$-6$	$3$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+(\beta _{1}+\beta _{4})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
4020.2.a.h	$7$	$32.100$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$-7$	$-7$	$3$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
4020.2.a.i	$7$	$32.100$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$7$	$7$	$1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-\beta _{4}q^{7}+q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4020))$ into lower level spaces

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	4020.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 9 \)
Sturm bound:			\(1632\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

\(2\)	\(3\)	\(5\)	\(67\)	Fricke	Dim.
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(4\)
Plus space				\(+\)	\(18\)
Minus space				\(-\)	\(26\)

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	67	$q$-expansion
4020.2.a.a	\(1\)	\(32.100\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4020.2.a.b	\(4\)	\(32.100\)	4.4.9301.1	None	\(0\)	\(-4\)	\(-4\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4020.2.a.c	\(4\)	\(32.100\)	4.4.98117.1	None	\(0\)	\(4\)	\(-4\)	\(1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
4020.2.a.d	\(4\)	\(32.100\)	\(\Q(\zeta_{15})^+\)	None	\(0\)	\(4\)	\(4\)	\(-3\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots\)
4020.2.a.e	\(5\)	\(32.100\)	5.5.1257629.1	None	\(0\)	\(-5\)	\(5\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
4020.2.a.f	\(6\)	\(32.100\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(0\)	\(-6\)	\(6\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{5})q^{11}+\cdots\)
4020.2.a.g	\(6\)	\(32.100\)	6.6.195727752.1	None	\(0\)	\(6\)	\(-6\)	\(3\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+(\beta _{1}+\beta _{4})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
4020.2.a.h	\(7\)	\(32.100\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(-7\)	\(-7\)	\(3\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
4020.2.a.i	\(7\)	\(32.100\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(7\)	\(7\)	\(1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-\beta _{4}q^{7}+q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4020))\) 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	4020.2.a

Level	4020
Weight	2
Character orbit	a
Rep. character	\(\chi_{4020}(1,\cdot)\)
Character field	\(\Q\)
Dimension	44
Newforms	9
Sturm bound	1632
Trace bound	5