Space of modular forms of level 1025, weight 1, and Character 1025.i

• Label: 1025.1.i
• Level: $1025$
• Weight: $1$
• Character orbit: 1025.i
• Rep. character: $\chi_{1025}(132,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $105$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1025 = 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1025.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 205 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(105\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1025, [\chi])\).

	Total	New	Old
Modular forms	14	6	8
Cusp forms	2	2	0
Eisenstein series	12	4	8

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1025, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1025.1.i.a	$1025$	$1$	1025.i	205.i	$4$	$2$	$1$	$0.512$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{4}-q^{9}+(1-i)q^{11}-q^{16}+(1+\cdots)q^{19}+\cdots\)