Space of modular forms of level 164, weight 5, and Character 164.d

• Label: 164.5.d
• Level: $164$
• Weight: $5$
• Character orbit: 164.d
• Rep. character: $\chi_{164}(163,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $6$
• Sturm bound: $105$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(105\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(164, [\chi])\).

	Total	New	Old
Modular forms	86	86	0
Cusp forms	82	82	0
Eisenstein series	4	4	0

Trace form

82 * q - 2 * q^2 - 2 * q^4 + 20 * q^5 + 34 * q^8 + 2214 * q^9 - 384 * q^10 - 282 * q^16 + 350 * q^18 - 136 * q^20 + 280 * q^21 + 8406 * q^25 - 1982 * q^32 + 3512 * q^33 - 3562 * q^36 + 1396 * q^37 - 6440 * q^40 + 2482 * q^41 + 12836 * q^42 - 388 * q^45 - 5680 * q^46 + 21030 * q^49 - 3246 * q^50 - 2120 * q^57 - 2204 * q^61 - 3936 * q^62 + 6406 * q^64 - 36652 * q^66 - 1798 * q^72 + 13748 * q^73 + 6176 * q^74 - 9608 * q^77 - 20496 * q^78 - 4936 * q^80 + 79018 * q^81 - 38962 * q^82 - 948 * q^84 - 20400 * q^86 - 53504 * q^90 - 2784 * q^92 + 22110 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(164, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
164.5.d.a	$164$	$5$	164.d	164.d	$2$	$2$	$2$	$16.953$	\(\Q(\sqrt{41}) \)	\(\Q(\sqrt{-41}) \)	✓	✓			164.5.d.a	$2$	$0$	\(-8\)	\(-22\)	\(0\)	\(138\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+(-11-\beta )q^{3}+2^{4}q^{4}+6\beta q^{5}+\cdots\)
164.5.d.b	$164$	$5$	164.d	164.d	$2$	$2$	$2$	$16.953$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			164.5.d.b	$4$	$0$	\(-8\)	\(0\)	\(28\)	\(0\)	$2^{4}\cdot 3\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+2^{4}q^{4}+14q^{5}-2^{6}q^{8}-3^{4}q^{9}+\cdots\)
164.5.d.c	$164$	$5$	164.d	164.d	$2$	$2$	$2$	$16.953$	\(\Q(\sqrt{41}) \)	\(\Q(\sqrt{-41}) \)	✓	✓			164.5.d.a	$2$	$0$	\(-8\)	\(22\)	\(0\)	\(-138\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+(11-\beta )q^{3}+2^{4}q^{4}-6\beta q^{5}+\cdots\)
164.5.d.d	$164$	$5$	164.d	164.d	$2$	$2$	$2$	$16.953$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-41}) \)	✓	✓			164.5.d.d	$4$	$0$	\(8\)	\(0\)	\(-64\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}+11\beta q^{3}+2^{4}q^{4}-2^{5}q^{5}+\cdots\)
164.5.d.e	$164$	$5$	164.d	164.d	$2$	$2$	$2$	$16.953$	\(\Q(\sqrt{82}) \)	\(\Q(\sqrt{-41}) \)	✓	✓			164.5.d.e	$4$	$0$	\(8\)	\(0\)	\(64\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}+\beta q^{3}+2^{4}q^{4}+2^{5}q^{5}+4\beta q^{6}+\cdots\)
164.5.d.f	$164$	$5$	164.d	164.d	$2$	$72$	$72$	$16.953$		None		✓	✓		164.5.d.f	$4$	$0$	\(6\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$