LMFDB - Space of Modular Forms of Level 619, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 619 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	619.a (trivial)
Character field:			$\Q$
Newforms:			$ 2 $
Sturm bound:			$103$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(619))$.

	Total	New
Modular forms	52	52
Cusp forms	51	51
Eisenstein series	1	1

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

$619$	Dim.
$+$	$21$
$-$	$30$

Trace form

$51q $ $\mathstrut -\mathstrut 4q^{3} $ $\mathstrut +\mathstrut 48q^{4} $ $\mathstrut -\mathstrut 2q^{7} $ $\mathstrut +\mathstrut 6q^{8} $ $\mathstrut +\mathstrut 49q^{9} $ $\mathstrut +\mathstrut 6q^{10} $ $\mathstrut -\mathstrut 4q^{11} $ $\mathstrut -\mathstrut 14q^{12} $ $\mathstrut -\mathstrut 2q^{13} $ $\mathstrut -\mathstrut 12q^{14} $ $\mathstrut -\mathstrut 12q^{15} $ $\mathstrut +\mathstrut 46q^{16} $ $\mathstrut -\mathstrut 10q^{17} $ $\mathstrut -\mathstrut 4q^{18} $ $\mathstrut -\mathstrut 16q^{19} $ $\mathstrut +\mathstrut 4q^{20} $ $\mathstrut -\mathstrut 12q^{21} $ $\mathstrut +\mathstrut 12q^{22} $ $\mathstrut -\mathstrut 10q^{23} $ $\mathstrut -\mathstrut 4q^{24} $ $\mathstrut +\mathstrut 51q^{25} $ $\mathstrut -\mathstrut 10q^{26} $ $\mathstrut -\mathstrut 10q^{27} $ $\mathstrut -\mathstrut 12q^{28} $ $\mathstrut +\mathstrut 12q^{29} $ $\mathstrut -\mathstrut 30q^{30} $ $\mathstrut -\mathstrut 6q^{31} $ $\mathstrut +\mathstrut 2q^{32} $ $\mathstrut -\mathstrut 12q^{33} $ $\mathstrut -\mathstrut 2q^{34} $ $\mathstrut +\mathstrut 6q^{35} $ $\mathstrut +\mathstrut 32q^{36} $ $\mathstrut -\mathstrut 4q^{37} $ $\mathstrut +\mathstrut 26q^{38} $ $\mathstrut +\mathstrut 28q^{39} $ $\mathstrut +\mathstrut 14q^{42} $ $\mathstrut -\mathstrut 2q^{43} $ $\mathstrut +\mathstrut 2q^{44} $ $\mathstrut -\mathstrut 6q^{45} $ $\mathstrut -\mathstrut 16q^{46} $ $\mathstrut -\mathstrut 8q^{47} $ $\mathstrut -\mathstrut 34q^{48} $ $\mathstrut +\mathstrut 47q^{49} $ $\mathstrut +\mathstrut 8q^{50} $ $\mathstrut -\mathstrut 8q^{51} $ $\mathstrut +\mathstrut 6q^{52} $ $\mathstrut -\mathstrut 2q^{53} $ $\mathstrut -\mathstrut 32q^{54} $ $\mathstrut +\mathstrut 6q^{55} $ $\mathstrut -\mathstrut 26q^{56} $ $\mathstrut -\mathstrut 32q^{57} $ $\mathstrut +\mathstrut 52q^{58} $ $\mathstrut -\mathstrut 4q^{59} $ $\mathstrut -\mathstrut 56q^{60} $ $\mathstrut -\mathstrut 6q^{61} $ $\mathstrut +\mathstrut 70q^{62} $ $\mathstrut -\mathstrut 46q^{63} $ $\mathstrut +\mathstrut 86q^{64} $ $\mathstrut -\mathstrut 22q^{65} $ $\mathstrut -\mathstrut 30q^{66} $ $\mathstrut +\mathstrut 4q^{67} $ $\mathstrut -\mathstrut 68q^{68} $ $\mathstrut -\mathstrut 24q^{69} $ $\mathstrut +\mathstrut 4q^{70} $ $\mathstrut -\mathstrut 14q^{71} $ $\mathstrut +\mathstrut 18q^{72} $ $\mathstrut -\mathstrut 6q^{73} $ $\mathstrut +\mathstrut 4q^{74} $ $\mathstrut -\mathstrut 50q^{75} $ $\mathstrut -\mathstrut 46q^{76} $ $\mathstrut -\mathstrut 18q^{77} $ $\mathstrut -\mathstrut 20q^{78} $ $\mathstrut +\mathstrut 8q^{79} $ $\mathstrut +\mathstrut 36q^{80} $ $\mathstrut +\mathstrut 11q^{81} $ $\mathstrut +\mathstrut 4q^{82} $ $\mathstrut -\mathstrut 12q^{83} $ $\mathstrut -\mathstrut 56q^{84} $ $\mathstrut -\mathstrut 10q^{85} $ $\mathstrut -\mathstrut 34q^{86} $ $\mathstrut +\mathstrut 24q^{87} $ $\mathstrut +\mathstrut 14q^{88} $ $\mathstrut +\mathstrut 46q^{89} $ $\mathstrut +\mathstrut 58q^{90} $ $\mathstrut -\mathstrut 34q^{91} $ $\mathstrut +\mathstrut 28q^{92} $ $\mathstrut -\mathstrut 30q^{93} $ $\mathstrut -\mathstrut 12q^{94} $ $\mathstrut +\mathstrut 6q^{95} $ $\mathstrut -\mathstrut 56q^{96} $ $\mathstrut +\mathstrut 12q^{97} $ $\mathstrut +\mathstrut 24q^{98} $ $\mathstrut -\mathstrut 46q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(619))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	619	$q$-expansion
619.2.a.a	$21$	$4.943$		None	$-9$	$-5$	$-21$	$-4$	$+$
619.2.a.b	$30$	$4.943$		None	$9$	$1$	$21$	$2$	$-$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 619 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	619.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 2 \)
Sturm bound:			\(103\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

\(619\)	Dim.
\(+\)	\(21\)
\(-\)	\(30\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	619	$q$-expansion
619.2.a.a	\(21\)	\(4.943\)		None	\(-9\)	\(-5\)	\(-21\)	\(-4\)	\(+\)
619.2.a.b	\(30\)	\(4.943\)		None	\(9\)	\(1\)	\(21\)	\(2\)	\(-\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\) 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	619.2.a

Level	619
Weight	2
Character orbit	a
Rep. character	\(\chi_{619}(1,\cdot)\)
Character field	\(\Q\)
Dimension	51
Newforms	2
Sturm bound	103
Trace bound	1