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

• Label: 930.2.i
• Level: $930$
• Weight: $2$
• Character orbit: 930.i
• Rep. character: $\chi_{930}(211,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $14$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	400	40	360
Cusp forms	368	40	328
Eisenstein series	32	0	32

Trace form

\( 40 q + 40 q^{4} - 20 q^{9} + O(q^{10}) \)

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.i.a	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-1\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots\)
930.2.i.b	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(1\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.c	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(1\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.d	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.e	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.f	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.g	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.h	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(1\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.i	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(1\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.j	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(-4\)	\(-2\)	\(-2\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
930.2.i.k	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(-2\)	\(2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.l	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(4\)	\(-2\)	\(2\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.m	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(4\)	\(2\)	\(-2\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.n	$930$	$2$	930.i	31.c	$3$	$6$	$3$	$7.426$	6.0.3636603.4	None		$2$	$0$	\(-6\)	\(3\)	\(-3\)	\(-4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)

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

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