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

• Label: 608.2.bh
• Level: $608$
• Weight: $2$
• Character orbit: 608.bh
• Rep. character: $\chi_{608}(15,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $108$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.bh (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
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	132	396
Cusp forms	432	108	324
Eisenstein series	96	24	72

Trace form

\( 108 q + 12 q^{3} - 12 q^{9} + O(q^{10}) \)

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
608.2.bh.a	$608$	$2$	608.bh	152.v	$18$	$12$	$2$	$4.855$	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(1+\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}-\beta _{8})q^{3}+\cdots\)
608.2.bh.b	$608$	$2$	608.bh	152.v	$18$	$96$	$16$	$4.855$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)