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

• Label: 930.2.n
• Level: $930$
• Weight: $2$
• Character orbit: 930.n
• Rep. character: $\chi_{930}(481,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	800	96	704
Cusp forms	736	96	640
Eisenstein series	64	0	64

Trace form

\( 96 q - 4 q^{3} - 24 q^{4} - 8 q^{7} - 24 q^{9} + O(q^{10}) \)

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.n.a	$930$	$2$	930.n	31.d	$5$	$8$	$2$	$7.426$	8.0.13140625.1	None		$2$	$0$	\(-2\)	\(2\)	\(8\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{4}q^{4}+q^{5}-q^{6}+\cdots\)
930.2.n.b	$930$	$2$	930.n	31.d	$5$	$8$	$2$	$7.426$	8.0.1816890625.5	None		$2$	$0$	\(2\)	\(2\)	\(-8\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
930.2.n.c	$930$	$2$	930.n	31.d	$5$	$12$	$3$	$7.426$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-3\)	\(-3\)	\(-12\)	\(-1\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{8}q^{4}-q^{5}+q^{6}+\cdots\)
930.2.n.d	$930$	$2$	930.n	31.d	$5$	$12$	$3$	$7.426$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-3\)	\(3\)	\(-12\)	\(-1\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{3}+\beta _{5}-\beta _{6})q^{2}+\beta _{5}q^{3}+\cdots\)
930.2.n.e	$930$	$2$	930.n	31.d	$5$	$12$	$3$	$7.426$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(3\)	\(-3\)	\(12\)	\(-1\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-1-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.n.f	$930$	$2$	930.n	31.d	$5$	$12$	$3$	$7.426$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(3\)	\(3\)	\(12\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{8}q^{2}-\beta _{6}q^{3}+(-1-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
930.2.n.g	$930$	$2$	930.n	31.d	$5$	$16$	$4$	$7.426$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-4\)	\(-4\)	\(16\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}-\beta _{7}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.n.h	$930$	$2$	930.n	31.d	$5$	$16$	$4$	$7.426$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(4\)	\(-4\)	\(-16\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}+\beta _{3}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)