Space of modular forms of level 162, weight 6, and Character 162.c

• Label: 162.6.c
• Level: $162$
• Weight: $6$
• Character orbit: 162.c
• Rep. character: $\chi_{162}(55,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $16$
• Sturm bound: $162$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(162\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(162, [\chi])\).

	Total	New	Old
Modular forms	294	40	254
Cusp forms	246	40	206
Eisenstein series	48	0	48

Trace form

40 * q - 320 * q^4 + 290 * q^7 - 1810 * q^13 - 5120 * q^16 + 2408 * q^19 + 1896 * q^22 - 19112 * q^25 - 9280 * q^28 + 6158 * q^31 + 7656 * q^34 - 91636 * q^37 - 16804 * q^43 + 37920 * q^46 + 9510 * q^49 - 28960 * q^52 - 198036 * q^55 + 25080 * q^58 + 39662 * q^61 + 163840 * q^64 - 10204 * q^67 - 60120 * q^70 + 41624 * q^73 - 19264 * q^76 - 155200 * q^79 + 42336 * q^82 - 14994 * q^85 + 30336 * q^88 - 248384 * q^91 + 96240 * q^94 + 268250 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(162, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.6.c.a	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					18.6.a.a	$2$	$0$	\(-4\)	\(0\)	\(-96\)	\(148\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-96\zeta_{6}q^{5}+\cdots\)
162.6.c.b	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.a	$2$	$0$	\(-4\)	\(0\)	\(-33\)	\(-59\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-33\zeta_{6}q^{5}+\cdots\)
162.6.c.c	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.b	$2$	$0$	\(-4\)	\(0\)	\(-24\)	\(-77\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-24\zeta_{6}q^{5}+\cdots\)
162.6.c.d	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None		✓			162.6.a.a	$2$	$0$	\(-4\)	\(0\)	\(-21\)	\(-74\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots\)
162.6.c.e	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					6.6.a.a	$2$	$0$	\(-4\)	\(0\)	\(66\)	\(-176\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+66\zeta_{6}q^{5}+\cdots\)
162.6.c.f	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.c	$2$	$0$	\(-4\)	\(0\)	\(84\)	\(193\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+84\zeta_{6}q^{5}+\cdots\)
162.6.c.g	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.c	$2$	$0$	\(4\)	\(0\)	\(-84\)	\(193\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-84\zeta_{6}q^{5}+\cdots\)
162.6.c.h	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					6.6.a.a	$2$	$0$	\(4\)	\(0\)	\(-66\)	\(-176\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-66\zeta_{6}q^{5}+\cdots\)
162.6.c.i	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None		✓			162.6.a.a	$2$	$0$	\(4\)	\(0\)	\(21\)	\(-74\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots\)
162.6.c.j	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.b	$2$	$1$	\(4\)	\(0\)	\(24\)	\(-77\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+24\zeta_{6}q^{5}+\cdots\)
162.6.c.k	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					54.6.a.a	$2$	$0$	\(4\)	\(0\)	\(33\)	\(-59\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+33\zeta_{6}q^{5}+\cdots\)
162.6.c.l	$162$	$6$	162.c	9.c	$3$	$2$	$1$	$25.982$	\(\Q(\sqrt{-3}) \)	None					18.6.a.a	$2$	$0$	\(4\)	\(0\)	\(96\)	\(148\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+96\zeta_{6}q^{5}+\cdots\)
162.6.c.m	$162$	$6$	162.c	9.c	$3$	$4$	$2$	$25.982$	\(\Q(\sqrt{-3}, \sqrt{-307})\)	None		✓			162.6.a.d	$2$	$0$	\(-8\)	\(0\)	\(12\)	\(14\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{1}q^{2}+(-2^{4}-2^{4}\beta _{1})q^{4}+(6+6\beta _{1}+\cdots)q^{5}+\cdots\)
162.6.c.n	$162$	$6$	162.c	9.c	$3$	$4$	$2$	$25.982$	\(\Q(\zeta_{12})\)	None		✓			162.6.a.c	$2$	$0$	\(-8\)	\(0\)	\(12\)	\(176\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4\beta_1-4)q^{2}-16\beta_1 q^{4}+(-5\beta_{2}+6\beta_1)q^{5}+\cdots\)
162.6.c.o	$162$	$6$	162.c	9.c	$3$	$4$	$2$	$25.982$	\(\Q(\sqrt{-3}, \sqrt{-307})\)	None		✓			162.6.a.d	$2$	$0$	\(8\)	\(0\)	\(-12\)	\(14\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\beta _{1}q^{2}+(-2^{4}-2^{4}\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
162.6.c.p	$162$	$6$	162.c	9.c	$3$	$4$	$2$	$25.982$	\(\Q(\zeta_{12})\)	None		✓			162.6.a.c	$2$	$0$	\(8\)	\(0\)	\(-12\)	\(176\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4\beta_1+4)q^{2}-16\beta_1 q^{4}+(-5\beta_{2}-6\beta_1)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)