Space of modular forms of level 804, weight 1, and Character 804.be

• Label: 804.1.be
• Level: $804$
• Weight: $1$
• Character orbit: 804.be
• Rep. character: $\chi_{804}(17,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $136$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	804.be (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(136\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(804, [\chi])\).

	Total	New	Old
Modular forms	140	20	120
Cusp forms	20	20	0
Eisenstein series	120	0	120

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 2 q^{3} + 2 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(804, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
804.1.be.a	$804$	$1$	804.be	201.o	$66$	$20$	$1$	$0.401$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q+\zeta_{66}^{30}q^{3}+(-\zeta_{66}^{17}+\zeta_{66}^{26}+\cdots)q^{7}+\cdots\)