Space of modular forms of level 417, weight 2, and Character 417.m

• Label: 417.2.m
• Level: $417$
• Weight: $2$
• Character orbit: 417.m
• Rep. character: $\chi_{417}(4,\cdot)$
• Character field: $\Q(\zeta_{69})$
• Dimension: $1012$
• Newform subspaces: $2$
• Sturm bound: $93$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 417 = 3 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	417.m (of order \(69\) and degree \(44\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 139 \)
Character field:			\(\Q(\zeta_{69})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(93\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(417, [\chi])\).

	Total	New	Old
Modular forms	2156	1012	1144
Cusp forms	1980	1012	968
Eisenstein series	176	0	176

Trace form

\( 1012 q + q^{3} + 20 q^{4} - 2 q^{5} + 4 q^{6} - 3 q^{7} + 23 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(417, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
417.2.m.a	$417$	$2$	417.m	139.g	$69$	$484$	$11$	$3.330$		None		✓			417.2.m.a	$2$	$0$	\(1\)	\(-11\)	\(-3\)	\(-1\)		$\mathrm{SU}(2)[C_{69}]$
417.2.m.b	$417$	$2$	417.m	139.g	$69$	$528$	$12$	$3.330$		None		✓	✓		417.2.m.b	$2$	$0$	\(-1\)	\(12\)	\(1\)	\(-2\)		$\mathrm{SU}(2)[C_{69}]$

Decomposition of \(S_{2}^{\mathrm{old}}(417, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(417, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(139, [\chi])\)\(^{\oplus 2}\)