Space of modular forms of level 17, weight 2, and trivial character

• Label: 17.2.a
• Level: $17$
• Weight: $2$
• Character orbit: 17.a
• Rep. character: $\chi_{17}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(17))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	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.

\(17\)	Dim.
\(-\)	\(1\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)