Space of modular forms of level 585, weight 2, and Character 585.h

• Label: 585.2.h
• Level: $585$
• Weight: $2$
• Character orbit: 585.h
• Rep. character: $\chi_{585}(64,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(585, [\chi])\).

	Total	New	Old
Modular forms	92	36	56
Cusp forms	76	32	44
Eisenstein series	16	4	12

Trace form

\( 32 q + 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.2.h.a	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+2q^{4}+(-2+i)q^{5}-3q^{7}+\cdots\)
585.2.h.b	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots\)
585.2.h.c	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}+(1+i)q^{5}-3q^{8}+(1+i)q^{10}+\cdots\)
585.2.h.d	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}+2q^{4}+(2-i)q^{5}+3q^{7}+(4+\cdots)q^{10}+\cdots\)
585.2.h.e	$585$	$2$	585.h	65.d	$2$	$4$	$4$	$4.671$	\(\Q(\sqrt{-5}, \sqrt{13})\)	\(\Q(\sqrt{-195}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots\)
585.2.h.f	$585$	$2$	585.h	65.d	$2$	$8$	$8$	$4.671$	8.0.\(\cdots\).21	\(\Q(\sqrt{-39}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{4}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
585.2.h.g	$585$	$2$	585.h	65.d	$2$	$12$	$12$	$4.671$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+(1+\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(585, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \)