Space of modular forms of level 2448, weight 1, and Character 2448.bd

• Label: 2448.1.bd
• Level: $2448$
• Weight: $1$
• Character orbit: 2448.bd
• Rep. character: $\chi_{2448}(1169,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2448.bd (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2448, [\chi])\).

	Total	New	Old
Modular forms	88	4	84
Cusp forms	40	4	36
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q + 4 q^{13} + 4 q^{31} + 4 q^{55} - 4 q^{73} + 4 q^{79} - 4 q^{85}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2448, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2448.1.bd.a	$2448$	$1$	2448.bd	51.f	$4$	$4$	$2$	$1.222$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None			✓	✓	612.1.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{11}+q^{13}-\zeta_{8}q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2448, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 2}\)