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

• Label: 804.2.y
• Level: $804$
• Weight: $2$
• Character orbit: 804.y
• Rep. character: $\chi_{804}(49,\cdot)$
• Character field: $\Q(\zeta_{33})$
• 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.y (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{33})\)
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	2840	220	2620
Cusp forms	2600	220	2380
Eisenstein series	240	0	240

Trace form

\( 220 q + 2 q^{3} - 2 q^{7} - 22 q^{9} + O(q^{10}) \)

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.y.a	$804$	$2$	804.y	67.g	$33$	$100$	$5$	$6.420$		None		$2$	$0$	\(0\)	\(-10\)	\(2\)	\(-3\)		$\mathrm{SU}(2)[C_{33}]$
804.2.y.b	$804$	$2$	804.y	67.g	$33$	$120$	$6$	$6.420$		None		$2$	$0$	\(0\)	\(12\)	\(-2\)	\(1\)		$\mathrm{SU}(2)[C_{33}]$

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

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