Space of modular forms of level 205, weight 2, and Character 205.b

• Label: 205.2.b
• Level: $205$
• Weight: $2$
• Character orbit: 205.b
• Rep. character: $\chi_{205}(124,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(205, [\chi])\).

	Total	New	Old
Modular forms	24	20	4
Cusp forms	20	20	0
Eisenstein series	4	0	4

Trace form

\( 20 q - 24 q^{4} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(205, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
205.2.b.a	$205$	$2$	205.b	5.b	$2$	$6$	$6$	$1.637$	6.0.839056.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
205.2.b.b	$205$	$2$	205.b	5.b	$2$	$14$	$14$	$1.637$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)