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 - 76 * q^10 - 368 * q^14 + 276 * q^16 - 168 * q^19 + 668 * q^20 + 96 * q^21 + 324 * q^24 - 204 * q^25 + 552 * q^26 - 1272 * q^29 - 336 * q^30 - 976 * q^31 + 1200 * q^34 + 72 * q^35 + 972 * q^36 + 336 * q^39 + 1788 * q^40 + 1128 * q^41 + 616 * q^44 + 252 * q^45 - 1344 * q^46 + 244 * q^49 + 2296 * q^50 - 744 * q^51 + 108 * q^54 - 192 * q^56 - 1968 * q^59 - 1032 * q^60 - 728 * q^61 - 2860 * q^64 - 3232 * q^65 - 528 * q^66 + 576 * q^69 + 1304 * q^70 + 576 * q^71 - 1760 * q^74 - 216 * q^75 + 2192 * q^76 - 2744 * q^79 - 3116 * q^80 + 2268 * q^81 - 6048 * q^84 + 1440 * q^85 - 2528 * q^86 + 3064 * q^89 + 684 * q^90 - 4608 * q^91 - 3632 * q^94 + 792 * q^95 + 6396 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.4.c.a	$165$	$4$	165.c	5.b	$2$	$14$	$14$	$9.735$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			165.4.c.a	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
165.4.c.b	$165$	$4$	165.c	5.b	$2$	$14$	$14$	$9.735$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			165.4.c.b	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{4}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-\beta _{8}q^{3}+(-2-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)

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

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