LMFDB - Space of Modular Forms of Level 3, Weight 6, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 3 $
Weight:	$ k $	=	$ 6 $
Character orbit:	$[\chi]$	=	3.a (trivial)
Character field:			$\Q$
Newforms:			$ 1 $
Sturm bound:			$2$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(\Gamma_0(3))$.

	Total	New	Old
Modular forms	3	1	2
Cusp forms	1	1	0
Eisenstein series	2	0	2

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

$3$	Dim.
$-$	$1$

Trace form

$q $ $\mathstrut -\mathstrut 6q^{2} $ $\mathstrut +\mathstrut 9q^{3} $ $\mathstrut +\mathstrut 4q^{4} $ $\mathstrut +\mathstrut 6q^{5} $ $\mathstrut -\mathstrut 54q^{6} $ $\mathstrut -\mathstrut 40q^{7} $ $\mathstrut +\mathstrut 168q^{8} $ $\mathstrut +\mathstrut 81q^{9} $ $\mathstrut -\mathstrut 36q^{10} $ $\mathstrut -\mathstrut 564q^{11} $ $\mathstrut +\mathstrut 36q^{12} $ $\mathstrut +\mathstrut 638q^{13} $ $\mathstrut +\mathstrut 240q^{14} $ $\mathstrut +\mathstrut 54q^{15} $ $\mathstrut -\mathstrut 1136q^{16} $ $\mathstrut +\mathstrut 882q^{17} $ $\mathstrut -\mathstrut 486q^{18} $ $\mathstrut -\mathstrut 556q^{19} $ $\mathstrut +\mathstrut 24q^{20} $ $\mathstrut -\mathstrut 360q^{21} $ $\mathstrut +\mathstrut 3384q^{22} $ $\mathstrut -\mathstrut 840q^{23} $ $\mathstrut +\mathstrut 1512q^{24} $ $\mathstrut -\mathstrut 3089q^{25} $ $\mathstrut -\mathstrut 3828q^{26} $ $\mathstrut +\mathstrut 729q^{27} $ $\mathstrut -\mathstrut 160q^{28} $ $\mathstrut +\mathstrut 4638q^{29} $ $\mathstrut -\mathstrut 324q^{30} $ $\mathstrut +\mathstrut 4400q^{31} $ $\mathstrut +\mathstrut 1440q^{32} $ $\mathstrut -\mathstrut 5076q^{33} $ $\mathstrut -\mathstrut 5292q^{34} $ $\mathstrut -\mathstrut 240q^{35} $ $\mathstrut +\mathstrut 324q^{36} $ $\mathstrut -\mathstrut 2410q^{37} $ $\mathstrut +\mathstrut 3336q^{38} $ $\mathstrut +\mathstrut 5742q^{39} $ $\mathstrut +\mathstrut 1008q^{40} $ $\mathstrut -\mathstrut 6870q^{41} $ $\mathstrut +\mathstrut 2160q^{42} $ $\mathstrut +\mathstrut 9644q^{43} $ $\mathstrut -\mathstrut 2256q^{44} $ $\mathstrut +\mathstrut 486q^{45} $ $\mathstrut +\mathstrut 5040q^{46} $ $\mathstrut -\mathstrut 18672q^{47} $ $\mathstrut -\mathstrut 10224q^{48} $ $\mathstrut -\mathstrut 15207q^{49} $ $\mathstrut +\mathstrut 18534q^{50} $ $\mathstrut +\mathstrut 7938q^{51} $ $\mathstrut +\mathstrut 2552q^{52} $ $\mathstrut +\mathstrut 33750q^{53} $ $\mathstrut -\mathstrut 4374q^{54} $ $\mathstrut -\mathstrut 3384q^{55} $ $\mathstrut -\mathstrut 6720q^{56} $ $\mathstrut -\mathstrut 5004q^{57} $ $\mathstrut -\mathstrut 27828q^{58} $ $\mathstrut -\mathstrut 18084q^{59} $ $\mathstrut +\mathstrut 216q^{60} $ $\mathstrut +\mathstrut 39758q^{61} $ $\mathstrut -\mathstrut 26400q^{62} $ $\mathstrut -\mathstrut 3240q^{63} $ $\mathstrut +\mathstrut 27712q^{64} $ $\mathstrut +\mathstrut 3828q^{65} $ $\mathstrut +\mathstrut 30456q^{66} $ $\mathstrut -\mathstrut 23068q^{67} $ $\mathstrut +\mathstrut 3528q^{68} $ $\mathstrut -\mathstrut 7560q^{69} $ $\mathstrut +\mathstrut 1440q^{70} $ $\mathstrut -\mathstrut 4248q^{71} $ $\mathstrut +\mathstrut 13608q^{72} $ $\mathstrut -\mathstrut 41110q^{73} $ $\mathstrut +\mathstrut 14460q^{74} $ $\mathstrut -\mathstrut 27801q^{75} $ $\mathstrut -\mathstrut 2224q^{76} $ $\mathstrut +\mathstrut 22560q^{77} $ $\mathstrut -\mathstrut 34452q^{78} $ $\mathstrut +\mathstrut 21920q^{79} $ $\mathstrut -\mathstrut 6816q^{80} $ $\mathstrut +\mathstrut 6561q^{81} $ $\mathstrut +\mathstrut 41220q^{82} $ $\mathstrut +\mathstrut 82452q^{83} $ $\mathstrut -\mathstrut 1440q^{84} $ $\mathstrut +\mathstrut 5292q^{85} $ $\mathstrut -\mathstrut 57864q^{86} $ $\mathstrut +\mathstrut 41742q^{87} $ $\mathstrut -\mathstrut 94752q^{88} $ $\mathstrut -\mathstrut 94086q^{89} $ $\mathstrut -\mathstrut 2916q^{90} $ $\mathstrut -\mathstrut 25520q^{91} $ $\mathstrut -\mathstrut 3360q^{92} $ $\mathstrut +\mathstrut 39600q^{93} $ $\mathstrut +\mathstrut 112032q^{94} $ $\mathstrut -\mathstrut 3336q^{95} $ $\mathstrut +\mathstrut 12960q^{96} $ $\mathstrut +\mathstrut 49442q^{97} $ $\mathstrut +\mathstrut 91242q^{98} $ $\mathstrut -\mathstrut 45684q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{6}^{\mathrm{new}}(\Gamma_0(3))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces					A-L signs	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$		3	$q$-expansion
3.6.a.a	$1$	$0.481$	$\Q$	None	$-6$	$9$	$6$	$-40$		$-$	$q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 3 \)
Weight:	\( k \)	=	\( 6 \)
Character orbit:	\([\chi]\)	=	3.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Label	Dim.	\(A\)	Field	CM	Traces					A-L signs	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)		3	$q$-expansion
3.6.a.a	\(1\)	\(0.481\)	\(\Q\)	None	\(-6\)	\(9\)	\(6\)	\(-40\)		\(-\)	\(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\) 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	3.6.a

Level	3
Weight	6
Character orbit	a
Rep. character	\(\chi_{3}(1,\cdot)\)
Character field	\(\Q\)
Dimension	1
Newforms	1
Sturm bound	2
Trace bound	0