Space of modular forms of level 165, weight 4, and Character 165.c

• Label: 165.4.c
• Level: $165$
• Weight: $4$
• Character orbit: 165.c
• Rep. character: $\chi_{165}(34,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(165, [\chi])\).

	Total	New	Old
Modular forms	76	28	48
Cusp forms	68	28	40
Eisenstein series	8	0	8

Trace form

\( 28 q - 108 q^{4} - 28 q^{5} - 12 q^{6} - 252 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.4.c.a	$165$	$4$	165.c	5.b	$2$	$14$	$14$	$9.735$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
165.4.c.b	$165$	$4$	165.c	5.b	$2$	$14$	$14$	$9.735$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{4}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-\beta _{8}q^{3}+(-2-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(165, [\chi]) \cong \)