Space of modular forms of level 42, weight 2, and Character 42.e

• Label: 42.2.e
• Level: $42$
• Weight: $2$
• Character orbit: 42.e
• Rep. character: $\chi_{42}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(42, [\chi])\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	8	4	4
Eisenstein series	16	0	16

Trace form

\( 4 q - 2 q^{4} - 4 q^{5} - 4 q^{6} + 6 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(42, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
42.2.e.a	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
42.2.e.b	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(-3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)