LMFDB - Space of Modular Forms of Level 23, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 23 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	23.a (trivial)
Character field:			$\Q$
Newforms:			$ 1 $
Sturm bound:			$4$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(23))$.

	Total	New
Modular forms	3	3
Cusp forms	2	2
Eisenstein series	1	1

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

$23$	Dim.
$-$	$2$

Trace form

$2q $ $\mathstrut -\mathstrut q^{2} $ $\mathstrut -\mathstrut q^{4} $ $\mathstrut -\mathstrut 2q^{5} $ $\mathstrut -\mathstrut 5q^{6} $ $\mathstrut +\mathstrut 2q^{7} $ $\mathstrut +\mathstrut 4q^{9} $ $\mathstrut +\mathstrut 6q^{10} $ $\mathstrut -\mathstrut 6q^{11} $ $\mathstrut +\mathstrut 5q^{12} $ $\mathstrut +\mathstrut 6q^{13} $ $\mathstrut +\mathstrut 4q^{14} $ $\mathstrut -\mathstrut 10q^{15} $ $\mathstrut -\mathstrut 3q^{16} $ $\mathstrut +\mathstrut 6q^{17} $ $\mathstrut -\mathstrut 2q^{18} $ $\mathstrut -\mathstrut 4q^{19} $ $\mathstrut -\mathstrut 4q^{20} $ $\mathstrut -\mathstrut 10q^{21} $ $\mathstrut -\mathstrut 2q^{22} $ $\mathstrut +\mathstrut 2q^{23} $ $\mathstrut +\mathstrut 10q^{24} $ $\mathstrut +\mathstrut 2q^{25} $ $\mathstrut -\mathstrut 3q^{26} $ $\mathstrut -\mathstrut 6q^{28} $ $\mathstrut -\mathstrut 6q^{29} $ $\mathstrut +\mathstrut 10q^{30} $ $\mathstrut +\mathstrut 9q^{32} $ $\mathstrut +\mathstrut 10q^{33} $ $\mathstrut -\mathstrut 8q^{34} $ $\mathstrut +\mathstrut 8q^{35} $ $\mathstrut -\mathstrut 2q^{36} $ $\mathstrut +\mathstrut 2q^{37} $ $\mathstrut +\mathstrut 2q^{38} $ $\mathstrut -\mathstrut 10q^{40} $ $\mathstrut +\mathstrut 2q^{41} $ $\mathstrut +\mathstrut 8q^{44} $ $\mathstrut -\mathstrut 4q^{45} $ $\mathstrut -\mathstrut q^{46} $ $\mathstrut -\mathstrut 15q^{48} $ $\mathstrut -\mathstrut 2q^{49} $ $\mathstrut -\mathstrut 11q^{50} $ $\mathstrut +\mathstrut 10q^{51} $ $\mathstrut -\mathstrut 3q^{52} $ $\mathstrut -\mathstrut 8q^{53} $ $\mathstrut +\mathstrut 5q^{54} $ $\mathstrut -\mathstrut 4q^{55} $ $\mathstrut -\mathstrut 10q^{56} $ $\mathstrut +\mathstrut 3q^{58} $ $\mathstrut +\mathstrut 4q^{59} $ $\mathstrut +\mathstrut 4q^{61} $ $\mathstrut +\mathstrut 15q^{62} $ $\mathstrut +\mathstrut 4q^{63} $ $\mathstrut +\mathstrut 4q^{64} $ $\mathstrut -\mathstrut 6q^{65} $ $\mathstrut +\mathstrut 10q^{66} $ $\mathstrut -\mathstrut 10q^{67} $ $\mathstrut +\mathstrut 2q^{68} $ $\mathstrut -\mathstrut 4q^{70} $ $\mathstrut +\mathstrut 20q^{71} $ $\mathstrut +\mathstrut 22q^{73} $ $\mathstrut -\mathstrut 6q^{74} $ $\mathstrut +\mathstrut 20q^{75} $ $\mathstrut +\mathstrut 2q^{76} $ $\mathstrut -\mathstrut 16q^{77} $ $\mathstrut -\mathstrut 15q^{78} $ $\mathstrut -\mathstrut 4q^{79} $ $\mathstrut +\mathstrut 18q^{80} $ $\mathstrut -\mathstrut 22q^{81} $ $\mathstrut -\mathstrut 11q^{82} $ $\mathstrut -\mathstrut 22q^{83} $ $\mathstrut +\mathstrut 10q^{84} $ $\mathstrut -\mathstrut 16q^{85} $ $\mathstrut +\mathstrut 10q^{88} $ $\mathstrut -\mathstrut 12q^{89} $ $\mathstrut +\mathstrut 12q^{90} $ $\mathstrut +\mathstrut 6q^{91} $ $\mathstrut -\mathstrut q^{92} $ $\mathstrut -\mathstrut 30q^{93} $ $\mathstrut -\mathstrut 5q^{94} $ $\mathstrut +\mathstrut 4q^{95} $ $\mathstrut -\mathstrut 5q^{96} $ $\mathstrut +\mathstrut 22q^{97} $ $\mathstrut +\mathstrut 11q^{98} $ $\mathstrut -\mathstrut 12q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(23))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces					A-L signs	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$		23	$q$-expansion
23.2.a.a	$2$	$0.184$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$-2$	$2$		$-$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	23.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

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	23.2.a

Level	23
Weight	2
Character orbit	a
Rep. character	\(\chi_{23}(1,\cdot)\)
Character field	\(\Q\)
Dimension	2
Newforms	1
Sturm bound	4
Trace bound	0

Label	Dim.	\(A\)	Field	CM	Traces					A-L signs	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)		23	$q$-expansion
23.2.a.a	\(2\)	\(0.184\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(-2\)	\(2\)		\(-\)	\(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)