Space of modular forms of level 1331, weight 1, and Character 1331.d

• Label: 1331.1.d
• Level: $1331$
• Weight: $1$
• Character orbit: 1331.d
• Rep. character: $\chi_{1331}(161,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $121$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1331 = 11^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1331.d (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(121\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1331, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	20	20	0
Eisenstein series	44	0	44

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

20 * q + q^3 - 5 * q^4 + q^5 - 4 * q^9 - 4 * q^12 + 2 * q^15 - 5 * q^16 + q^20 - 4 * q^23 - 4 * q^25 + 2 * q^27 + q^31 - 4 * q^36 + q^37 - 12 * q^45 + q^47 + q^48 - 5 * q^49 + q^53 + q^59 + 2 * q^60 - 5 * q^64 - 4 * q^67 + 2 * q^69 + q^71 + 3 * q^75 + q^80 - 3 * q^81 - 4 * q^89 + q^92 + 2 * q^93 + q^97

Decomposition of \(S_{1}^{\mathrm{new}}(1331, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1331.1.d.a	$1331$	$1$	1331.d	11.d	$10$	$20$	$5$	$0.664$	20.0.\(\cdots\).1	$D_{11}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	1331.1.b.a	$8$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q-\beta _{13}q^{3}+\beta _{9}q^{4}+(\beta _{8}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots\)