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

• Label: 804.2.s
• Level: $804$
• Weight: $2$
• Character orbit: 804.s
• Rep. character: $\chi_{804}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $220$
• Newform subspaces: $2$
• Sturm bound: $272$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(272\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1420	220	1200
Cusp forms	1300	220	1080
Eisenstein series	120	0	120

Trace form

\( 220 q - 4 q^{9} + O(q^{10}) \)

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.s.a	$804$	$2$	804.s	201.j	$22$	$20$	$2$	$6.420$	\(\Q(\zeta_{33})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{22}]$	\(q+\zeta_{33}^{13}q^{3}+(-2\zeta_{33}^{7}-2\zeta_{33}^{8}+\cdots)q^{7}+\cdots\)
804.2.s.b	$804$	$2$	804.s	201.j	$22$	$200$	$20$	$6.420$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)