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Space of modular forms of level 608, weight 2, and Character 608.y

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Properties

Label	608.2.y

Level	$608$
Weight	$2$
Character orbit	608.y
Rep. character	$\chi_{608}(161,\cdot)$
Character field	$\Q(\zeta_{9})$
Dimension	$120$
Newform subspaces	$4$
Sturm bound	$160$
Trace bound	$3$

Related objects

Newspace 608.2

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Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.y (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(608, [\chi])\).

	Total	New	Old
Modular forms	528	120	408
Cusp forms	432	120	312
Eisenstein series	96	0	96

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(608, [\chi])\) 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
608.2.y.a	$608$	$2$	608.y	19.e	$9$	$24$	$4$	$4.855$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
608.2.y.b	$608$	$2$	608.y	19.e	$9$	$30$	$5$	$4.855$		None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{9}]$
608.2.y.c	$608$	$2$	608.y	19.e	$9$	$30$	$5$	$4.855$		None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{9}]$
608.2.y.d	$608$	$2$	608.y	19.e	$9$	$36$	$6$	$4.855$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)