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

• Label: 804.2.g
• Level: $804$
• Weight: $2$
• Character orbit: 804.g
• Rep. character: $\chi_{804}(401,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $272$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	142	22	120
Cusp forms	130	22	108
Eisenstein series	12	0	12

Trace form

\( 22 q + 4 q^{9} + O(q^{10}) \)

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.g.a	$804$	$2$	804.g	201.d	$2$	$2$	$2$	$6.420$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
804.2.g.b	$804$	$2$	804.g	201.d	$2$	$4$	$4$	$6.420$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots\)
804.2.g.c	$804$	$2$	804.g	201.d	$2$	$16$	$16$	$6.420$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{12}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots\)

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

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