Space of modular forms of level 244, weight 1, and Character 244.u

• Label: 244.1.u
• Level: $244$
• Weight: $1$
• Character orbit: 244.u
• Rep. character: $\chi_{244}(15,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $31$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 244 = 2^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	244.u (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 244 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(31\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(244, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	8	8	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

8 * q + q^2 + q^4 - 6 * q^5 - 2 * q^8 - 2 * q^9 - 6 * q^10 + 2 * q^13 + q^16 + 2 * q^17 + q^18 + 2 * q^20 - 5 * q^25 + 2 * q^26 - q^29 - 4 * q^32 - 4 * q^34 + q^36 + 2 * q^37 - q^40 + 2 * q^41 - q^45 + q^49 + 10 * q^50 + 6 * q^52 - 3 * q^53 - 3 * q^58 + q^61 - 2 * q^64 - 2 * q^65 - 3 * q^68 + 8 * q^72 - q^73 + 4 * q^74 - q^80 - 2 * q^81 - q^82 - q^85 - 3 * q^89 - q^90 - q^97 - 2 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(244, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
244.1.u.a	$244$	$1$	244.u	244.u	$30$	$8$	$1$	$0.122$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	244.1.u.a	$4$	$0$	\(1\)	\(0\)	\(-6\)	\(0\)	$1$		\(q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{10}+\cdots)q^{5}+\cdots\)