Space of modular forms of level 441, weight 1, and Character 441.b

• Label: 441.1.b
• Level: $441$
• Weight: $1$
• Character orbit: 441.b
• Rep. character: $\chi_{441}(197,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	441.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(441, [\chi])\).

	Total	New	Old
Modular forms	18	2	16
Cusp forms	2	2	0
Eisenstein series	16	0	16

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

\( 2 q - 2 q^{4} - 2 q^{16} - 4 q^{22} + 2 q^{25} + 4 q^{46} + 4 q^{58} + 2 q^{64} - 4 q^{67} + 4 q^{79}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.1.b.a	$441$	$1$	441.b	3.b	$2$	$2$	$2$	$0.220$	\(\Q(\sqrt{-2}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	441.1.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots\)