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

• Label: 804.2.i
• Level: $804$
• Weight: $2$
• Character orbit: 804.i
• Rep. character: $\chi_{804}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $272$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(272\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	284	22	262
Cusp forms	260	22	238
Eisenstein series	24	0	24

Trace form

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

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.i.a	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{3}-2q^{5}+3\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
804.2.i.b	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{3}+2q^{5}-5\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\)
804.2.i.c	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{3}+2q^{5}+3\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots\)
804.2.i.d	$804$	$2$	804.i	67.c	$3$	$8$	$4$	$6.420$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\)
804.2.i.e	$804$	$2$	804.i	67.c	$3$	$8$	$4$	$6.420$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{3}+(-1-\beta _{2}+\beta _{5}-\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots\)

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

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