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

• Label: 930.2.d
• Level: $930$
• Weight: $2$
• Character orbit: 930.d
• Rep. character: $\chi_{930}(559,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $9$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	200	28	172
Cusp forms	184	28	156
Eisenstein series	16	0	16

Trace form

\( 28 q - 28 q^{4} + 8 q^{5} - 28 q^{9} + O(q^{10}) \)

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.d.a	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
930.2.d.b	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
930.2.d.c	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}+q^{6}+\cdots\)
930.2.d.d	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
930.2.d.e	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots\)
930.2.d.f	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
930.2.d.g	$930$	$2$	930.d	5.b	$2$	$4$	$4$	$7.426$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}q^{3}-q^{4}+(2+\zeta_{8})q^{5}+\cdots\)
930.2.d.h	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
930.2.d.i	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.11669056.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)