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

• Label: 608.2.i
• Level: $608$
• Weight: $2$
• Character orbit: 608.i
• Rep. character: $\chi_{608}(353,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
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	176	40	136
Cusp forms	144	40	104
Eisenstein series	32	0	32

Trace form

\( 40 q - 24 q^{9} + O(q^{10}) \)

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.i.a	$608$	$2$	608.i	19.c	$3$	$2$	$1$	$4.855$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+\cdots\)
608.2.i.b	$608$	$2$	608.i	19.c	$3$	$2$	$1$	$4.855$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+2q^{7}+\cdots\)
608.2.i.c	$608$	$2$	608.i	19.c	$3$	$8$	$4$	$4.855$	8.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(-4\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
608.2.i.d	$608$	$2$	608.i	19.c	$3$	$8$	$4$	$4.855$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{5}+(-2+2\beta _{1}+\cdots)q^{9}+\cdots\)
608.2.i.e	$608$	$2$	608.i	19.c	$3$	$8$	$4$	$4.855$	8.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(1+\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
608.2.i.f	$608$	$2$	608.i	19.c	$3$	$12$	$6$	$4.855$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{10}q^{5}+(\beta _{2}-\beta _{5}+\cdots)q^{7}+\cdots\)

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

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