Space of modular forms of level 930, weight 2, and Character 930.h

• Label: 930.2.h
• Level: $930$
• Weight: $2$
• Character orbit: 930.h
• Rep. character: $\chi_{930}(371,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 93 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

	Total	New	Old
Modular forms	200	40	160
Cusp forms	184	40	144
Eisenstein series	16	0	16

Trace form

\( 40 q - 40 q^{4} - 24 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
930.2.h.a	$930$	$2$	930.h	93.c	$2$	$4$	$4$	$7.426$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.h.b	$930$	$2$	930.h	93.c	$2$	$4$	$4$	$7.426$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots\)
930.2.h.c	$930$	$2$	930.h	93.c	$2$	$16$	$16$	$7.426$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.h.d	$930$	$2$	930.h	93.c	$2$	$16$	$16$	$7.426$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-\beta _{12}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{5}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)