Space of modular forms of level 165, weight 6, and Character 165.c

• Label: 165.6.c
• Level: $165$
• Weight: $6$
• Character orbit: 165.c
• Rep. character: $\chi_{165}(34,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(144\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(165, [\chi])\).

	Total	New	Old
Modular forms	124	52	72
Cusp forms	116	52	64
Eisenstein series	8	0	8

Trace form

52 * q - 876 * q^4 - 196 * q^5 + 180 * q^6 - 4212 * q^9 - 1708 * q^10 + 6736 * q^14 + 15284 * q^16 + 80 * q^19 + 6524 * q^20 + 360 * q^21 - 540 * q^24 + 10996 * q^25 + 9864 * q^26 - 14208 * q^29 + 2736 * q^30 + 38144 * q^31 - 8432 * q^34 + 5760 * q^35 + 70956 * q^36 - 11160 * q^39 + 5212 * q^40 + 40128 * q^41 + 4840 * q^44 + 15876 * q^45 - 48800 * q^46 - 192788 * q^49 - 52712 * q^50 - 10440 * q^51 - 14580 * q^54 - 273600 * q^56 + 149568 * q^59 + 113112 * q^60 - 93208 * q^61 - 585068 * q^64 - 73960 * q^65 + 34848 * q^66 - 98496 * q^69 + 169704 * q^70 + 47760 * q^71 + 452704 * q^74 + 38880 * q^75 - 262416 * q^76 + 36608 * q^79 + 171988 * q^80 + 341172 * q^81 - 54432 * q^84 - 87400 * q^85 + 103360 * q^86 + 628456 * q^89 + 138348 * q^90 + 300672 * q^91 + 587248 * q^94 - 243408 * q^95 - 476100 * q^96

Decomposition of \(S_{6}^{\mathrm{new}}(165, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.6.c.a	$165$	$6$	165.c	5.b	$2$	$26$	$26$	$26.463$		None		✓			165.6.c.a	$2$	$0$	\(0\)	\(0\)	\(-98\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
165.6.c.b	$165$	$6$	165.c	5.b	$2$	$26$	$26$	$26.463$		None		✓			165.6.c.b	$2$	$0$	\(0\)	\(0\)	\(-98\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)