Space of modular forms of level 1530, weight 2, and Character 1530.d

• Label: 1530.2.d
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.d
• Rep. character: $\chi_{1530}(919,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $10$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(648\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1530, [\chi])\).

	Total	New	Old
Modular forms	340	40	300
Cusp forms	308	40	268
Eisenstein series	32	0	32

Trace form

\( 40 q - 40 q^{4} - 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1530, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1530.2.d.a	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-2+i)q^{5}+iq^{8}+\cdots\)
1530.2.d.b	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{8}+\cdots\)
1530.2.d.c	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2+i)q^{5}+4iq^{7}-iq^{8}+\cdots\)
1530.2.d.d	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots\)
1530.2.d.e	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1530.2.d.f	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1530.2.d.g	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1530.2.d.h	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1530.2.d.i	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
1530.2.d.j	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1530, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)