Space of modular forms of level 1205, weight 2, and Character 1205.b

• Label: 1205.2.b
• Level: $1205$
• Weight: $2$
• Character orbit: 1205.b
• Rep. character: $\chi_{1205}(724,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $242$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(242\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1205, [\chi])\).

	Total	New	Old
Modular forms	124	120	4
Cusp forms	120	120	0
Eisenstein series	4	0	4

Trace form

\( 120 q - 120 q^{4} - 120 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1205, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1205.2.b.a	$1205$	$2$	1205.b	5.b	$2$	$4$	$4$	$9.622$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}-3q^{4}+\cdots\)
1205.2.b.b	$1205$	$2$	1205.b	5.b	$2$	$4$	$4$	$9.622$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots\)
1205.2.b.c	$1205$	$2$	1205.b	5.b	$2$	$46$	$46$	$9.622$		None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1205.2.b.d	$1205$	$2$	1205.b	5.b	$2$	$66$	$66$	$9.622$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$