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

• Label: 1530.2.f
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.f
• Rep. character: $\chi_{1530}(1189,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $12$
• Sturm bound: $648$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(648\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	340	44	296
Cusp forms	308	44	264
Eisenstein series	32	0	32

Trace form

\( 44 q - 44 q^{4} + O(q^{10}) \)

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.f.a	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-2+i)q^{5}-4q^{7}+\cdots\)
1530.2.f.b	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2-i)q^{5}+2q^{7}+\cdots\)
1530.2.f.c	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2+i)q^{5}+4q^{7}+\cdots\)
1530.2.f.d	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(2+i)q^{5}-4q^{7}+iq^{8}+\cdots\)
1530.2.f.e	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2+i)q^{5}-2q^{7}-iq^{8}+\cdots\)
1530.2.f.f	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2+i)q^{5}+4q^{7}-iq^{8}+\cdots\)
1530.2.f.g	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1530.2.f.h	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+(3\zeta_{8}+\cdots)q^{7}+\cdots\)
1530.2.f.i	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
1530.2.f.j	$1530$	$2$	1530.f	85.c	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1530.2.f.k	$1530$	$2$	1530.f	85.c	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
1530.2.f.l	$1530$	$2$	1530.f	85.c	$2$	$8$	$8$	$12.217$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{6}q^{5}-\zeta_{24}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \)