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

• Label: 165.2.c
• Level: $165$
• Weight: $2$
• Character orbit: 165.c
• Rep. character: $\chi_{165}(34,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(48\)
Trace bound:			\(4\)
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	12	16
Cusp forms	20	12	8
Eisenstein series	8	0	8

Trace form

12 * q - 12 * q^4 + 4 * q^5 - 4 * q^6 - 12 * q^9 + 12 * q^10 - 16 * q^14 + 4 * q^16 + 16 * q^19 + 4 * q^20 - 8 * q^21 + 12 * q^24 - 4 * q^25 - 24 * q^26 + 16 * q^30 - 16 * q^34 + 12 * q^36 + 8 * q^39 - 28 * q^40 + 8 * q^44 - 4 * q^45 + 32 * q^46 - 12 * q^49 + 8 * q^50 - 8 * q^51 + 4 * q^54 + 96 * q^56 - 8 * q^60 - 40 * q^61 - 44 * q^64 + 40 * q^65 + 8 * q^66 - 16 * q^70 - 48 * q^71 + 32 * q^74 - 64 * q^76 + 32 * q^79 - 52 * q^80 + 12 * q^81 + 40 * q^85 - 16 * q^86 - 40 * q^89 - 12 * q^90 + 48 * q^94 - 48 * q^95 - 28 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.2.c.a	$165$	$2$	165.c	5.b	$2$	$6$	$6$	$1.318$	6.0.350464.1	None		✓			165.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
165.2.c.b	$165$	$2$	165.c	5.b	$2$	$6$	$6$	$1.318$	6.0.350464.1	None		✓			165.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)