Space of modular forms of level 1449, weight 1, and Character 1449.bu

• Label: 1449.1.bu
• Level: $1449$
• Weight: $1$
• Character orbit: 1449.bu
• Rep. character: $\chi_{1449}(125,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1449.bu (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 483 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1449, [\chi])\).

	Total	New	Old
Modular forms	120	40	80
Cusp forms	40	40	0
Eisenstein series	80	0	80

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	40	0	0	0

Trace form

\( 40 q + 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1449, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1449.1.bu.a	$1449$	$1$	1449.bu	483.w	$22$	$40$	$4$	$0.723$	\(\Q(\zeta_{88})\)	$D_{44}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{88}^{5}-\zeta_{88}^{7})q^{2}+(\zeta_{88}^{10}+\zeta_{88}^{12}+\cdots)q^{4}+\cdots\)