Space of modular forms of level 6030, weight 2, and Character 6030.d

• Label: 6030.2.d
• Level: $6030$
• Weight: $2$
• Character orbit: 6030.d
• Rep. character: $\chi_{6030}(2411,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $12$
• Sturm bound: $2448$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6030.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2448\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6030, [\chi])\).

	Total	New	Old
Modular forms	1240	96	1144
Cusp forms	1208	96	1112
Eisenstein series	32	0	32

Trace form

\( 96 q + 96 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6030, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6030.2.d.a	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-6q^{11}+\cdots\)
6030.2.d.b	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+q^{5}+2\beta q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.c	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
6030.2.d.d	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+q^{5}+\beta q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.e	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.f	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
6030.2.d.g	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{5}+2\beta q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.h	$6030$	$2$	6030.d	201.d	$2$	$2$	$2$	$48.150$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+6q^{11}+\cdots\)
6030.2.d.i	$6030$	$2$	6030.d	201.d	$2$	$16$	$16$	$48.150$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-16\)	\(0\)	\(16\)	\(0\)	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+q^{5}+\beta _{12}q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.j	$6030$	$2$	6030.d	201.d	$2$	$16$	$16$	$48.150$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(16\)	\(0\)	\(-16\)	\(0\)	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{5}+\beta _{12}q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.k	$6030$	$2$	6030.d	201.d	$2$	$24$	$24$	$48.150$		None		$2$	$0$	\(-24\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
6030.2.d.l	$6030$	$2$	6030.d	201.d	$2$	$24$	$24$	$48.150$		None		$2$	$0$	\(24\)	\(0\)	\(24\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6030, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6030, [\chi]) \cong \)