Space of modular forms of level 30, weight 6, and Character 30.e

• Label: 30.6.e
• Level: $30$
• Weight: $6$
• Character orbit: 30.e
• Rep. character: $\chi_{30}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(30, [\chi])\).

	Total	New	Old
Modular forms	68	20	48
Cusp forms	52	20	32
Eisenstein series	16	0	16

Trace form

\( 20 q - 4 q^{3} + 80 q^{6} + 76 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(30, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
30.6.e.a	$30$	$6$	30.e	15.e	$4$	$20$	$10$	$4.812$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(76\)	$2^{25}\cdot 3^{14}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+2^{4}\beta _{5}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)