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

• Label: 1530.2.m
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.m
• Rep. character: $\chi_{1530}(647,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $9$
• Sturm bound: $648$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(648\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	680	64	616
Cusp forms	616	64	552
Eisenstein series	64	0	64

Trace form

\( 64 q - 16 q^{7} + O(q^{10}) \)

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.m.a	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
1530.2.m.b	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
1530.2.m.c	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1530.2.m.d	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
1530.2.m.e	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1530.2.m.f	$1530$	$2$	1530.m	15.e	$4$	$4$	$2$	$12.217$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2+\zeta_{8}^{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1530.2.m.g	$1530$	$2$	1530.m	15.e	$4$	$8$	$4$	$12.217$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(-\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1530.2.m.h	$1530$	$2$	1530.m	15.e	$4$	$16$	$8$	$12.217$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}-\beta _{9}q^{4}-\beta _{11}q^{5}+(\beta _{2}-\beta _{9}+\cdots)q^{7}+\cdots\)
1530.2.m.i	$1530$	$2$	1530.m	15.e	$4$	$16$	$8$	$12.217$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{8}q^{2}-\beta _{9}q^{4}+(\beta _{2}+\beta _{5}-\beta _{6}+\beta _{15})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)