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

• Label: 930.2.bt
• Level: $930$
• Weight: $2$
• Character orbit: 930.bt
• Rep. character: $\chi_{930}(13,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $512$
• Newform subspaces: $2$
• 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.bt (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 2 \)
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	3200	512	2688
Cusp forms	2944	512	2432
Eisenstein series	256	0	256

Trace form

\( 512 q + 24 q^{7} + O(q^{10}) \)

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.bt.a	$930$	$2$	930.bt	155.x	$60$	$256$	$16$	$7.426$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{60}]$
930.2.bt.b	$930$	$2$	930.bt	155.x	$60$	$256$	$16$	$7.426$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{60}]$

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

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