Space of modular forms of level 164, weight 1, and Character 164.j

• Label: 164.1.j
• Level: $164$
• Weight: $1$
• Character orbit: 164.j
• Rep. character: $\chi_{164}(51,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	164.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(164, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

4 * q - q^2 - q^4 - 2 * q^5 - q^8 + 4 * q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 + 3 * q^20 - 3 * q^25 + 3 * q^26 - 2 * q^29 + 4 * q^32 + 3 * q^34 - q^36 + 3 * q^37 - 2 * q^40 - q^41 - 2 * q^45 - q^49 + 2 * q^50 + 3 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 + q^65 - 2 * q^68 - q^72 - 2 * q^73 + 3 * q^74 + 3 * q^80 + 4 * q^81 - q^82 + 6 * q^85 - 2 * q^89 - 2 * q^90 + 3 * q^97 - q^98

Decomposition of \(S_{1}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
164.1.j.a	$164$	$1$	164.j	164.j	$10$	$4$	$1$	$0.082$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	164.1.j.a	$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots\)