Space of modular forms of level 164, weight 3, and Character 164.p

• Label: 164.3.p
• Level: $164$
• Weight: $3$
• Character orbit: 164.p
• Rep. character: $\chi_{164}(13,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	164.p (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(63\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(164, [\chi])\).

	Total	New	Old
Modular forms	720	112	608
Cusp forms	624	112	512
Eisenstein series	96	0	96

Trace form

112 * q + 8 * q^3 - 24 * q^9 - 36 * q^13 - 12 * q^15 + 56 * q^17 + 48 * q^19 - 52 * q^21 - 52 * q^27 + 52 * q^29 + 180 * q^31 + 304 * q^33 + 184 * q^35 + 68 * q^37 + 64 * q^39 - 4 * q^41 + 80 * q^43 - 400 * q^45 - 436 * q^47 - 144 * q^49 - 580 * q^51 - 120 * q^53 + 88 * q^55 - 56 * q^57 - 144 * q^61 + 88 * q^63 + 108 * q^65 - 704 * q^67 - 980 * q^69 - 584 * q^71 - 412 * q^73 - 748 * q^75 - 692 * q^77 + 140 * q^79 - 520 * q^83 + 928 * q^85 + 580 * q^87 + 828 * q^89 + 1316 * q^91 + 512 * q^93 + 916 * q^95 + 644 * q^97 + 888 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(164, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
164.3.p.a	$164$	$3$	164.p	41.h	$40$	$112$	$7$	$4.469$		None		✓	✓	✓	164.3.p.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{40}]$

Decomposition of \(S_{3}^{\mathrm{old}}(164, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(164, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 2}\)