Space of modular forms of level 162, weight 7, and Character 162.b

• Label: 162.7.b
• Level: $162$
• Weight: $7$
• Character orbit: 162.b
• Rep. character: $\chi_{162}(161,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $189$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(189\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(162, [\chi])\).

	Total	New	Old
Modular forms	174	24	150
Cusp forms	150	24	126
Eisenstein series	24	0	24

Trace form

\( 24 q - 768 q^{4} + 480 q^{7} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(162, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.7.b.a	$162$	$7$	162.b	3.b	$2$	$4$	$4$	$37.269$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			162.7.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4\beta _{1}q^{2}-2^{5}q^{4}+(70\beta _{1}-5^{2}\beta _{2}+\cdots)q^{5}+\cdots\)
162.7.b.b	$162$	$7$	162.b	3.b	$2$	$8$	$8$	$37.269$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			162.7.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(964\)	$2^{2}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta _{1}q^{2}-2^{5}q^{4}+(12\beta _{1}+\beta _{3})q^{5}+\cdots\)
162.7.b.c	$162$	$7$	162.b	3.b	$2$	$12$	$12$	$37.269$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		18.7.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-480\)	$2^{16}\cdot 3^{42}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2^{5}q^{4}+\beta _{8}q^{5}+(-40-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)