Space of modular forms of level 3248, weight 1, and Character 3248.bu

• Label: 3248.1.bu
• Level: $3248$
• Weight: $1$
• Character orbit: 3248.bu
• Rep. character: $\chi_{3248}(2145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3248 = 2^{4} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3248.bu (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 203 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3248, [\chi])\).

	Total	New	Old
Modular forms	32	6	26
Cusp forms	8	2	6
Eisenstein series	24	4	20

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

\( 2 q - 3 q^{5} - q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3248, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3248.1.bu.a	$3248$	$1$	3248.bu	203.i	$6$	$2$	$1$	$1.621$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{29}) \)			✓	✓	812.1.o.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$		\(q+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3248, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3248, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(812, [\chi])\)\(^{\oplus 3}\)