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

• Label: 804.2.ba
• Level: $804$
• Weight: $2$
• Character orbit: 804.ba
• Rep. character: $\chi_{804}(41,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $460$
• 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.ba (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{66})\)
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	460	2380
Cusp forms	2600	460	2140
Eisenstein series	240	0	240

Trace form

\( 460 q - 6 q^{7} + 10 q^{9} + O(q^{10}) \)

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.ba.a	$804$	$2$	804.ba	201.p	$66$	$20$	$1$	$6.420$	\(\Q(\zeta_{33})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{U}(1)[D_{66}]$	\(q+(-2\zeta_{33}-\zeta_{33}^{12})q^{3}+(1-\zeta_{33}+\cdots)q^{7}+\cdots\)
804.2.ba.b	$804$	$2$	804.ba	201.p	$66$	$440$	$22$	$6.420$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{66}]$

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

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