Space of modular forms of level 619, weight 2, and trivial character

• Label: 619.2.a
• Level: $619$
• Weight: $2$
• Character orbit: 619.a
• Rep. character: $\chi_{619}(1,\cdot)$
• Character field: $\Q$
• Dimension: $51$
• Newform subspaces: $2$
• Sturm bound: $103$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
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	Old
Modular forms	52	52	0
Cusp forms	51	51	0
Eisenstein series	1	1	0

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

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

Trace form

\( 51 q - 4 q^{3} + 48 q^{4} - 2 q^{7} + 6 q^{8} + 49 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		619
619.2.a.a	$619$	$2$	619.a	1.a	$1$	$21$	$21$	$4.943$		None	✓	$1$	$1$	\(-9\)	\(-5\)	\(-21\)	\(-4\)		$+$	$+$		$\mathrm{SU}(2)$
619.2.a.b	$619$	$2$	619.a	1.a	$1$	$30$	$30$	$4.943$		None	✓	$1$	$0$	\(9\)	\(1\)	\(21\)	\(2\)		$-$	$-$		$\mathrm{SU}(2)$