Space of modular forms of level 930, weight 4, and Character 930.d

• Label: 930.4.d
• Level: $930$
• Weight: $4$
• Character orbit: 930.d
• Rep. character: $\chi_{930}(559,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $5$
• Sturm bound: $768$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(768\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(930, [\chi])\).

	Total	New	Old
Modular forms	584	92	492
Cusp forms	568	92	476
Eisenstein series	16	0	16

Trace form

\( 92 q - 368 q^{4} - 8 q^{5} - 828 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(930, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
930.4.d.a	$930$	$4$	930.d	5.b	$2$	$2$	$2$	$54.872$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}+(10+5i)q^{5}+\cdots\)
930.4.d.b	$930$	$4$	930.d	5.b	$2$	$20$	$20$	$54.872$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{3}q^{2}+3\beta _{3}q^{3}-4q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
930.4.d.c	$930$	$4$	930.d	5.b	$2$	$20$	$20$	$54.872$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{8}q^{2}-3\beta _{8}q^{3}-4q^{4}-\beta _{16}q^{5}+\cdots\)
930.4.d.d	$930$	$4$	930.d	5.b	$2$	$24$	$24$	$54.872$		None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
930.4.d.e	$930$	$4$	930.d	5.b	$2$	$26$	$26$	$54.872$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)