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

• Label: 804.2.j
• Level: $804$
• Weight: $2$
• Character orbit: 804.j
• Rep. character: $\chi_{804}(499,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• Newform subspaces: $2$
• Sturm bound: $272$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 268 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(272\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	280	136	144
Cusp forms	264	136	128
Eisenstein series	16	0	16

Trace form

\( 136 q - 4 q^{4} + 136 q^{9} + O(q^{10}) \)

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.j.a	$804$	$2$	804.j	268.h	$6$	$68$	$34$	$6.420$		None		$2$	$0$	\(0\)	\(-68\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$
804.2.j.b	$804$	$2$	804.j	268.h	$6$	$68$	$34$	$6.420$		None		$2$	$0$	\(0\)	\(68\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$

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

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