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

• Label: 930.2.bg
• Level: $930$
• Weight: $2$
• Character orbit: 930.bg
• Rep. character: $\chi_{930}(121,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $160$
• Newform subspaces: $9$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	1600	160	1440
Cusp forms	1472	160	1312
Eisenstein series	128	0	128

Trace form

\( 160 q - 40 q^{4} + 20 q^{9} + O(q^{10}) \)

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.bg.a	$930$	$2$	930.bg	31.g	$15$	$8$	$1$	$7.426$	\(\Q(\zeta_{15})\)	None		$2$	$0$	\(-2\)	\(-1\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+\zeta_{15}^{3}q^{2}-\zeta_{15}^{7}q^{3}+\zeta_{15}^{6}q^{4}+\cdots\)
930.2.bg.b	$930$	$2$	930.bg	31.g	$15$	$16$	$2$	$7.426$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-2\)	\(-8\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q-\beta _{5}q^{2}+\beta _{10}q^{3}+(-1+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.bg.c	$930$	$2$	930.bg	31.g	$15$	$16$	$2$	$7.426$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-2\)	\(8\)	\(11\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{4}+\beta _{7}+\beta _{8}+\beta _{9}-\beta _{10})q^{2}+\beta _{10}q^{3}+\cdots\)
930.2.bg.d	$930$	$2$	930.bg	31.g	$15$	$16$	$2$	$7.426$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-4\)	\(2\)	\(8\)	\(11\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+\beta _{4}q^{2}+(\beta _{5}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
930.2.bg.e	$930$	$2$	930.bg	31.g	$15$	$16$	$2$	$7.426$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(4\)	\(-2\)	\(8\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+\beta _{9}q^{2}+(-1+\beta _{3}+\beta _{4}-\beta _{6}+\beta _{9}+\cdots)q^{3}+\cdots\)
930.2.bg.f	$930$	$2$	930.bg	31.g	$15$	$16$	$2$	$7.426$	16.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(2\)	\(-8\)	\(-13\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1-\beta _{11}-\beta _{13}+\beta _{15})q^{2}+(-\beta _{3}+\cdots)q^{3}+\cdots\)
930.2.bg.g	$930$	$2$	930.bg	31.g	$15$	$24$	$3$	$7.426$		None		$2$	$0$	\(-6\)	\(3\)	\(-12\)	\(9\)		$\mathrm{SU}(2)[C_{15}]$
930.2.bg.h	$930$	$2$	930.bg	31.g	$15$	$24$	$3$	$7.426$		None		$2$	$0$	\(6\)	\(-3\)	\(-12\)	\(-11\)		$\mathrm{SU}(2)[C_{15}]$
930.2.bg.i	$930$	$2$	930.bg	31.g	$15$	$24$	$3$	$7.426$		None		$2$	$0$	\(6\)	\(3\)	\(12\)	\(-7\)		$\mathrm{SU}(2)[C_{15}]$

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

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