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

• Label: 825.2.by
• Level: $825$
• Weight: $2$
• Character orbit: 825.by
• Rep. character: $\chi_{825}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $240$
• 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.by (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{10})\)
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	496	240	256
Cusp forms	464	240	224
Eisenstein series	32	0	32

Trace form

\( 240 q + 60 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{7} + 60 q^{9} + O(q^{10}) \)

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.by.a	$825$	$2$	825.by	275.aa	$10$	$240$	$60$	$6.588$		None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)