Space of modular forms of level 2804, weight 1, and Character 2804.d

• Label: 2804.1.d
• Level: $2804$
• Weight: $1$
• Character orbit: 2804.d
• Rep. character: $\chi_{2804}(2803,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $351$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2804 = 2^{2} \cdot 701 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2804.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2804 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(351\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2804, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	16	16	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 16 q^{4} - 2 q^{5} - 2 q^{6} + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2804, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2804.1.d.a	$2804$	$1$	2804.d	2804.d	$2$	$8$	$8$	$1.399$	\(\Q(\zeta_{34})^+\)	$D_{17}$	\(\Q(\sqrt{-701}) \)	None	✓	✓			2804.1.d.a	$2$	$0$	\(-8\)	\(1\)	\(-1\)	\(0\)	$1$		\(q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{2}q^{6}+\cdots\)
2804.1.d.b	$2804$	$1$	2804.d	2804.d	$2$	$8$	$8$	$1.399$	\(\Q(\zeta_{34})^+\)	$D_{17}$	\(\Q(\sqrt{-701}) \)	None	✓	✓			2804.1.d.a	$2$	$0$	\(8\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+\beta _{6}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{6}q^{6}+\cdots\)