Space of modular forms of level 825, weight 2, and Character 825.df

• Label: 825.2.df
• Level: $825$
• Weight: $2$
• Character orbit: 825.df
• Rep. character: $\chi_{825}(47,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $928$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.df (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 825 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

	Total	New	Old
Modular forms	992	992	0
Cusp forms	928	928	0
Eisenstein series	64	64	0

Trace form

\( 928 q - 8 q^{3} - 20 q^{4} - 12 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.2.df.a	$825$	$2$	825.df	825.cf	$20$	$928$	$116$	$6.588$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$