Space of modular forms of level 617, weight 2, and trivial character

• Label: 617.2.a
• Level: $617$
• Weight: $2$
• Character orbit: 617.a
• Rep. character: $\chi_{617}(1,\cdot)$
• Character field: $\Q$
• Dimension: $51$
• Newform subspaces: $2$
• Sturm bound: $103$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	617.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 \(M_{2}(\Gamma_0(617))\).

	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.

\(617\)	Dim
\(+\)	\(23\)
\(-\)	\(28\)

Trace form

\( 51 q - 3 q^{2} - 2 q^{3} + 47 q^{4} - 4 q^{5} + 2 q^{7} - 9 q^{8} + 49 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(617))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		617
617.2.a.a	$617$	$2$	617.a	1.a	$1$	$23$	$23$	$4.927$		None	✓	$1$	$1$	\(-6\)	\(-13\)	\(-6\)	\(-37\)		$+$	$+$		$\mathrm{SU}(2)$
617.2.a.b	$617$	$2$	617.a	1.a	$1$	$28$	$28$	$4.927$		None	✓	$1$	$0$	\(3\)	\(11\)	\(2\)	\(39\)		$-$	$-$		$\mathrm{SU}(2)$