Space of modular forms of level 165, weight 2, and Character 165.f

• Label: 165.2.f
• Level: $165$
• Weight: $2$
• Character orbit: 165.f
• Rep. character: $\chi_{165}(131,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(165, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	20	16	4
Eisenstein series	8	0	8

Trace form

\( 16 q - 4 q^{3} + 16 q^{4} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(165, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.2.f.a	$165$	$2$	165.f	33.d	$2$	$8$	$8$	$1.318$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
165.2.f.b	$165$	$2$	165.f	33.d	$2$	$8$	$8$	$1.318$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \)