Space of modular forms of level 2808, weight 1, and Character 2808.b

• Label: 2808.1.b
• Level: $2808$
• Weight: $1$
• Character orbit: 2808.b
• Rep. character: $\chi_{2808}(701,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $504$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2808.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 312 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(504\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2808, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	24	12	12
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2808, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2808.1.b.a	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-78}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{8}-q^{13}+q^{16}+q^{19}+\cdots\)
2808.1.b.b	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-78}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{8}+q^{13}+q^{16}-q^{19}+\cdots\)
2808.1.b.c	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-78}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+q^{19}+\cdots\)
2808.1.b.d	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-78}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}+q^{13}+q^{16}-q^{19}+\cdots\)
2808.1.b.e	$2808$	$1$	2808.b	312.b	$2$	$8$	$8$	$1.401$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2808, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2808, [\chi]) \cong \)