LMFDB - Space of Modular Forms of Level 24, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	24.a (trivial)
Character field:			$\Q$
Newforms:			$ 1 $
Sturm bound:			$8$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(24))$.

	Total	New	Old
Modular forms	8	1	7
Cusp forms	1	1	0
Eisenstein series	7	0	7

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

$2$	$3$	Fricke	Dim.
$-$	$+$	$-$	$1$
Plus space		$+$	$0$
Minus space		$-$	$1$

Trace form

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

$q $ $\mathstrut -\mathstrut q^{3} $ $\mathstrut -\mathstrut 2q^{5} $ $\mathstrut +\mathstrut q^{9} $ $\mathstrut +\mathstrut 4q^{11} $ $\mathstrut -\mathstrut 2q^{13} $ $\mathstrut +\mathstrut 2q^{15} $ $\mathstrut +\mathstrut 2q^{17} $ $\mathstrut -\mathstrut 4q^{19} $ $\mathstrut -\mathstrut 8q^{23} $ $\mathstrut -\mathstrut q^{25} $ $\mathstrut -\mathstrut q^{27} $ $\mathstrut +\mathstrut 6q^{29} $ $\mathstrut +\mathstrut 8q^{31} $ $\mathstrut -\mathstrut 4q^{33} $ $\mathstrut +\mathstrut 6q^{37} $ $\mathstrut +\mathstrut 2q^{39} $ $\mathstrut -\mathstrut 6q^{41} $ $\mathstrut +\mathstrut 4q^{43} $ $\mathstrut -\mathstrut 2q^{45} $ $\mathstrut -\mathstrut 7q^{49} $ $\mathstrut -\mathstrut 2q^{51} $ $\mathstrut -\mathstrut 2q^{53} $ $\mathstrut -\mathstrut 8q^{55} $ $\mathstrut +\mathstrut 4q^{57} $ $\mathstrut +\mathstrut 4q^{59} $ $\mathstrut -\mathstrut 2q^{61} $ $\mathstrut +\mathstrut 4q^{65} $ $\mathstrut -\mathstrut 4q^{67} $ $\mathstrut +\mathstrut 8q^{69} $ $\mathstrut +\mathstrut 8q^{71} $ $\mathstrut +\mathstrut 10q^{73} $ $\mathstrut +\mathstrut q^{75} $ $\mathstrut -\mathstrut 8q^{79} $ $\mathstrut +\mathstrut q^{81} $ $\mathstrut -\mathstrut 4q^{83} $ $\mathstrut -\mathstrut 4q^{85} $ $\mathstrut -\mathstrut 6q^{87} $ $\mathstrut -\mathstrut 6q^{89} $ $\mathstrut -\mathstrut 8q^{93} $ $\mathstrut +\mathstrut 8q^{95} $ $\mathstrut +\mathstrut 2q^{97} $ $\mathstrut +\mathstrut 4q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(24))$ 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	$q$-expansion
24.2.a.a	$1$	$0.192$	$\Q$	None	$0$	$-1$	$-2$	$0$		$-$	$+$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	24.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

\(2\)	\(3\)	Fricke	Dim.
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(1\)

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	$q$-expansion
24.2.a.a	\(1\)	\(0.192\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)		\(-\)	\(+\)	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\) 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	24.2.a

Level	24
Weight	2
Character orbit	a
Rep. character	\(\chi_{24}(1,\cdot)\)
Character field	\(\Q\)
Dimension	1
Newforms	1
Sturm bound	8
Trace bound	0