Space of modular forms of level 162, weight 5, and Character 162.b

• Label: 162.5.b
• Level: $162$
• Weight: $5$
• Character orbit: 162.b
• Rep. character: $\chi_{162}(161,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $135$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(135\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(162, [\chi])\).

	Total	New	Old
Modular forms	120	16	104
Cusp forms	96	16	80
Eisenstein series	24	0	24

Trace form

16 * q - 128 * q^4 - 52 * q^7 - 192 * q^10 + 260 * q^13 + 1024 * q^16 + 716 * q^19 - 672 * q^22 - 1916 * q^25 + 416 * q^28 + 1484 * q^31 - 1728 * q^34 - 5008 * q^37 + 1536 * q^40 + 3584 * q^43 + 2112 * q^46 - 3516 * q^49 - 2080 * q^52 + 11340 * q^55 + 1920 * q^58 + 9308 * q^61 - 8192 * q^64 - 10648 * q^67 + 2496 * q^70 - 1876 * q^73 - 5728 * q^76 - 19636 * q^79 + 4992 * q^82 + 27288 * q^85 + 5376 * q^88 - 39572 * q^91 + 15168 * q^94 - 20176 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(162, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.5.b.a	$162$	$5$	162.b	3.b	$2$	$4$	$4$	$16.746$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			162.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}-8q^{4}+(-17\beta _{1}+5\beta _{2}+\cdots)q^{5}+\cdots\)
162.5.b.b	$162$	$5$	162.b	3.b	$2$	$4$	$4$	$16.746$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			162.5.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{2}-8q^{4}+(-8\beta _{1}+\beta _{2})q^{5}+\cdots\)
162.5.b.c	$162$	$5$	162.b	3.b	$2$	$8$	$8$	$16.746$	8.0.\(\cdots\).4	None			✓		18.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(52\)	$2^{8}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-8q^{4}-\beta _{4}q^{5}+(6+\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)