LMFDB - Space of Modular Forms of Level 572, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	572.a (trivial)
Character field:			$\Q$
Newforms:			$ 5 $
Sturm bound:			$168$
Trace bound:			$5$
Distinguishing $T_p$:			$3$, $5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(572))$.

	Total	New	Old
Modular forms	90	10	80
Cusp forms	79	10	69
Eisenstein series	11	0	11

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

$2$	$11$	$13$	Fricke	Dim.
$-$	$+$	$+$	$-$	$2$
$-$	$+$	$-$	$+$	$2$
$-$	$-$	$+$	$+$	$3$
$-$	$-$	$-$	$-$	$3$
Plus space			$+$	$5$
Minus space			$-$	$5$

Trace form

$10q $ $\mathstrut -\mathstrut 2q^{3} $ $\mathstrut +\mathstrut 2q^{5} $ $\mathstrut +\mathstrut 16q^{9} $ $\mathstrut +\mathstrut O(q^{10}) $

$10q $ $\mathstrut -\mathstrut 2q^{3} $ $\mathstrut +\mathstrut 2q^{5} $ $\mathstrut +\mathstrut 16q^{9} $ $\mathstrut +\mathstrut 2q^{11} $ $\mathstrut -\mathstrut 10q^{15} $ $\mathstrut -\mathstrut 16q^{17} $ $\mathstrut -\mathstrut 4q^{19} $ $\mathstrut +\mathstrut 4q^{21} $ $\mathstrut -\mathstrut 10q^{23} $ $\mathstrut -\mathstrut 2q^{27} $ $\mathstrut -\mathstrut 8q^{29} $ $\mathstrut -\mathstrut 14q^{31} $ $\mathstrut +\mathstrut 2q^{33} $ $\mathstrut +\mathstrut 4q^{35} $ $\mathstrut +\mathstrut 2q^{37} $ $\mathstrut +\mathstrut 4q^{41} $ $\mathstrut +\mathstrut 8q^{43} $ $\mathstrut +\mathstrut 4q^{45} $ $\mathstrut -\mathstrut 8q^{47} $ $\mathstrut +\mathstrut 30q^{49} $ $\mathstrut -\mathstrut 4q^{51} $ $\mathstrut -\mathstrut 16q^{53} $ $\mathstrut -\mathstrut 6q^{55} $ $\mathstrut -\mathstrut 28q^{57} $ $\mathstrut +\mathstrut 18q^{59} $ $\mathstrut +\mathstrut 20q^{61} $ $\mathstrut +\mathstrut 8q^{63} $ $\mathstrut -\mathstrut 4q^{65} $ $\mathstrut -\mathstrut 6q^{67} $ $\mathstrut +\mathstrut 10q^{69} $ $\mathstrut -\mathstrut 26q^{71} $ $\mathstrut -\mathstrut 20q^{73} $ $\mathstrut +\mathstrut 12q^{75} $ $\mathstrut -\mathstrut 4q^{77} $ $\mathstrut -\mathstrut 4q^{79} $ $\mathstrut -\mathstrut 6q^{81} $ $\mathstrut -\mathstrut 36q^{85} $ $\mathstrut +\mathstrut 12q^{87} $ $\mathstrut +\mathstrut 2q^{89} $ $\mathstrut +\mathstrut 4q^{91} $ $\mathstrut +\mathstrut 10q^{93} $ $\mathstrut +\mathstrut 60q^{95} $ $\mathstrut +\mathstrut 2q^{97} $ $\mathstrut -\mathstrut 4q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(572))$ 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	11	13	$q$-expansion
572.2.a.a	$1$	$4.567$	$\Q$	None	$0$	$1$	$3$	$2$	$-$	$-$	$-$	$q+q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots$
572.2.a.b	$2$	$4.567$	$\Q(\sqrt{13}) $	None	$0$	$-3$	$0$	$-3$	$-$	$+$	$-$	$q+(-1-\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
572.2.a.c	$2$	$4.567$	$\Q(\sqrt{21}) $	None	$0$	$1$	$-4$	$3$	$-$	$-$	$-$	$q+\beta q^{3}-2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots$
572.2.a.d	$2$	$4.567$	$\Q(\sqrt{21}) $	None	$0$	$1$	$4$	$5$	$-$	$+$	$+$	$q+\beta q^{3}+2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots$
572.2.a.e	$3$	$4.567$	3.3.229.1	None	$0$	$-2$	$-1$	$-7$	$-$	$-$	$+$	$q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(572))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(572)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(26))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(44))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(52))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(143))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(286))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	572.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 5 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

\(2\)	\(11\)	\(13\)	Fricke	Dim.
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(3\)
Plus space			\(+\)	\(5\)
Minus space			\(-\)	\(5\)

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	11	13	$q$-expansion
572.2.a.a	\(1\)	\(4.567\)	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\)
572.2.a.b	\(2\)	\(4.567\)	\(\Q(\sqrt{13}) \)	None	\(0\)	\(-3\)	\(0\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q+(-1-\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
572.2.a.c	\(2\)	\(4.567\)	\(\Q(\sqrt{21}) \)	None	\(0\)	\(1\)	\(-4\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q+\beta q^{3}-2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.d	\(2\)	\(4.567\)	\(\Q(\sqrt{21}) \)	None	\(0\)	\(1\)	\(4\)	\(5\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{3}+2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.e	\(3\)	\(4.567\)	3.3.229.1	None	\(0\)	\(-2\)	\(-1\)	\(-7\)	\(-\)	\(-\)	\(+\)	\(q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(572))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(572))\) 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	572.2.a

Level	572
Weight	2
Character orbit	a
Rep. character	\(\chi_{572}(1,\cdot)\)
Character field	\(\Q\)
Dimension	10
Newforms	5
Sturm bound	168
Trace bound	5