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

• Label: 1530.2.r
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.r
• Rep. character: $\chi_{1530}(917,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $648$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(648\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	680	72	608
Cusp forms	616	72	544
Eisenstein series	64	0	64

Trace form

\( 72 q + O(q^{10}) \)

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.r.a	$1530$	$2$	1530.r	255.o	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
1530.2.r.b	$1530$	$2$	1530.r	255.o	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2+\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{8}+\cdots\)
1530.2.r.c	$1530$	$2$	1530.r	255.o	$4$	$24$	$12$	$12.217$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1530.2.r.d	$1530$	$2$	1530.r	255.o	$4$	$40$	$20$	$12.217$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)