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

• Label: 930.2.y
• Level: $930$
• Weight: $2$
• Character orbit: 930.y
• Rep. character: $\chi_{930}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 465 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	800	256	544
Cusp forms	736	256	480
Eisenstein series	64	0	64

Trace form

\( 256 q - 64 q^{4} - 8 q^{9} + O(q^{10}) \)

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.y.a	$930$	$2$	930.y	465.w	$10$	$128$	$32$	$7.426$		None		$4$	$0$	\(-32\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
930.2.y.b	$930$	$2$	930.y	465.w	$10$	$128$	$32$	$7.426$		None		$4$	$0$	\(32\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \)