Space of modular forms of level 550, weight 2, and Character 550.t

• Label: 550.2.t
• Level: $550$
• Weight: $2$
• Character orbit: 550.t
• Rep. character: $\chi_{550}(89,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $104$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.t (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).

	Total	New	Old
Modular forms	376	104	272
Cusp forms	344	104	240
Eisenstein series	32	0	32

Trace form

\( 104 q + 26 q^{4} + 8 q^{5} + 34 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
550.2.t.a	$550$	$2$	550.t	25.e	$10$	$8$	$2$	$4.392$	\(\Q(\zeta_{20})\)	None		$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\zeta_{20}q^{2}+(1+\zeta_{20}-\zeta_{20}^{3}-\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
550.2.t.b	$550$	$2$	550.t	25.e	$10$	$40$	$10$	$4.392$		None		$2$	$0$	\(0\)	\(-10\)	\(16\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
550.2.t.c	$550$	$2$	550.t	25.e	$10$	$56$	$14$	$4.392$		None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)