Space of modular forms of level 18, weight 42, and Character 18.c

• Label: 18.42.c
• Level: $18$
• Weight: $42$
• Character orbit: 18.c
• Rep. character: $\chi_{18}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $82$
• Newform subspaces: $2$
• Sturm bound: $126$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(126\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(18, [\chi])\).

	Total	New	Old
Modular forms	250	82	168
Cusp forms	242	82	160
Eisenstein series	8	0	8

Trace form

\( 82 q - 1048576 q^{2} - 10420079643 q^{3} - 45079976738816 q^{4} - 114052535967708 q^{5} - 1234600895447040 q^{6} - 9555429699348682 q^{7} + 2305843009213693952 q^{8} + 116965043728771007055 q^{9} + O(q^{10}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.42.c.a	$18$	$42$	18.c	9.c	$3$	$40$	$20$	$191.649$		None		✓			18.42.c.a	$2$	$0$	\(20971520\)	\(-5043516516\)	\(-57\!\cdots\!54\)	\(34\!\cdots\!20\)		$\mathrm{SU}(2)[C_{3}]$
18.42.c.b	$18$	$42$	18.c	9.c	$3$	$42$	$21$	$191.649$		None		✓	✓		18.42.c.b	$2$	$0$	\(-22020096\)	\(-5376563127\)	\(-57\!\cdots\!54\)	\(-43\!\cdots\!02\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{42}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{42}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{42}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)