Space of modular forms of level 1206, weight 2, and Character 1206.d

• Label: 1206.2.d
• Level: $1206$
• Weight: $2$
• Character orbit: 1206.d
• Rep. character: $\chi_{1206}(1205,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $408$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1206 = 2 \cdot 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1206.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(408\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1206, [\chi])\).

	Total	New	Old
Modular forms	212	20	192
Cusp forms	196	20	176
Eisenstein series	16	0	16

Trace form

\( 20 q + 20 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1206, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1206.2.d.a	$1206$	$2$	1206.d	201.d	$2$	$2$	$2$	$9.630$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-3\beta q^{7}-q^{8}-3\beta q^{13}+\cdots\)
1206.2.d.b	$1206$	$2$	1206.d	201.d	$2$	$2$	$2$	$9.630$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+3\beta q^{7}+q^{8}+3\beta q^{13}+\cdots\)
1206.2.d.c	$1206$	$2$	1206.d	201.d	$2$	$8$	$8$	$9.630$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots\)
1206.2.d.d	$1206$	$2$	1206.d	201.d	$2$	$8$	$8$	$9.630$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1206, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1206, [\chi]) \cong \)