Space of modular forms of level 804, weight 2, and Character 804.o

• Label: 804.2.o
• Level: $804$
• Weight: $2$
• Character orbit: 804.o
• Rep. character: $\chi_{804}(365,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $46$
• Newform subspaces: $4$
• Sturm bound: $272$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(272\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

	Total	New	Old
Modular forms	284	46	238
Cusp forms	260	46	214
Eisenstein series	24	0	24

Trace form

\( 46 q + 6 q^{7} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
804.2.o.a	$804$	$2$	804.o	201.f	$6$	$2$	$1$	$6.420$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{7}+\cdots\)
804.2.o.b	$804$	$2$	804.o	201.f	$6$	$4$	$2$	$6.420$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-4\)	\(8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{3}+2q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.c	$804$	$2$	804.o	201.f	$6$	$4$	$2$	$6.420$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(4\)	\(-8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{3})q^{3}-2q^{5}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.d	$804$	$2$	804.o	201.f	$6$	$36$	$18$	$6.420$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \)