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

• Label: 804.2.u
• Level: $804$
• Weight: $2$
• Character orbit: 804.u
• Rep. character: $\chi_{804}(43,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $680$
• 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.u (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 268 \)
Character field:			\(\Q(\zeta_{22})\)
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	1400	680	720
Cusp forms	1320	680	640
Eisenstein series	80	0	80

Trace form

\( 680 q - 4 q^{4} + 66 q^{8} - 68 q^{9} + O(q^{10}) \)

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.u.a	$804$	$2$	804.u	268.j	$22$	$340$	$34$	$6.420$		None		$2$	$0$	\(0\)	\(-34\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{22}]$
804.2.u.b	$804$	$2$	804.u	268.j	$22$	$340$	$34$	$6.420$		None		$2$	$0$	\(0\)	\(34\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)