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

• Label: 804.2.q
• Level: $804$
• Weight: $2$
• Character orbit: 804.q
• Rep. character: $\chi_{804}(25,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $120$
• 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.q (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
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	1420	120	1300
Cusp forms	1300	120	1180
Eisenstein series	120	0	120

Trace form

\( 120 q - 12 q^{9} + O(q^{10}) \)

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.q.a	$804$	$2$	804.q	67.e	$11$	$60$	$6$	$6.420$		None		$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{11}]$
804.2.q.b	$804$	$2$	804.q	67.e	$11$	$60$	$6$	$6.420$		None		$2$	$0$	\(0\)	\(6\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)