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.

\(17\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(-\)		\(2\)	\(2\)	\(0\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

q - q^2 - q^4 - 2 * q^5 + 4 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 - 2 * q^13 - 4 * q^14 - q^16 + q^17 + 3 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^23 - q^25 + 2 * q^26 - 4 * q^28 + 6 * q^29 + 4 * q^31 - 5 * q^32 - q^34 - 8 * q^35 + 3 * q^36 - 2 * q^37 + 4 * q^38 - 6 * q^40 - 6 * q^41 + 4 * q^43 + 6 * q^45 - 4 * q^46 + 9 * q^49 + q^50 + 2 * q^52 + 6 * q^53 + 12 * q^56 - 6 * q^58 - 12 * q^59 - 10 * q^61 - 4 * q^62 - 12 * q^63 + 7 * q^64 + 4 * q^65 + 4 * q^67 - q^68 + 8 * q^70 - 4 * q^71 - 9 * q^72 - 6 * q^73 + 2 * q^74 + 4 * q^76 + 12 * q^79 + 2 * q^80 + 9 * q^81 + 6 * q^82 - 4 * q^83 - 2 * q^85 - 4 * q^86 + 10 * q^89 - 6 * q^90 - 8 * q^91 - 4 * q^92 + 8 * q^95 + 2 * q^97 - 9 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓	✓	✓	17.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)