Space of modular forms of level 664, weight 2, and Character 664.i

• Label: 664.2.i
• Level: $664$
• Weight: $2$
• Character orbit: 664.i
• Rep. character: $\chi_{664}(9,\cdot)$
• Character field: $\Q(\zeta_{41})$
• Dimension: $840$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 664 = 2^{3} \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	664.i (of order \(41\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 83 \)
Character field:			\(\Q(\zeta_{41})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(664, [\chi])\).

	Total	New	Old
Modular forms	3520	840	2680
Cusp forms	3200	840	2360
Eisenstein series	320	0	320

Trace form

\( 840 q + 2 q^{3} + 2 q^{5} + 4 q^{7} - 23 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(664, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
664.2.i.a	$664$	$2$	664.i	83.c	$41$	$400$	$10$	$5.302$		None		✓			664.2.i.a	$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{41}]$
664.2.i.b	$664$	$2$	664.i	83.c	$41$	$440$	$11$	$5.302$		None		✓	✓		664.2.i.b	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$\mathrm{SU}(2)[C_{41}]$

Decomposition of \(S_{2}^{\mathrm{old}}(664, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(664, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(83, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(166, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(332, [\chi])\)\(^{\oplus 2}\)