Space of modular forms of level 608, weight 3, and Character 608.q

• Label: 608.3.q
• Level: $608$
• Weight: $3$
• Character orbit: 608.q
• Rep. character: $\chi_{608}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	608.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(608, [\chi])\).

	Total	New	Old
Modular forms	336	80	256
Cusp forms	304	80	224
Eisenstein series	32	0	32

Trace form

80 * q + 112 * q^9 - 16 * q^13 - 48 * q^17 + 48 * q^21 - 200 * q^25 - 88 * q^33 + 160 * q^37 - 88 * q^41 - 688 * q^49 + 16 * q^53 - 96 * q^57 + 64 * q^61 - 512 * q^65 + 56 * q^73 - 256 * q^77 - 136 * q^81 - 112 * q^85 + 240 * q^89 + 48 * q^93 + 152 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
608.3.q.a	$608$	$3$	608.q	76.g	$6$	$40$	$20$	$16.567$		None		✓			608.3.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
608.3.q.b	$608$	$3$	608.q	76.g	$6$	$40$	$20$	$16.567$		None		✓			608.3.q.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

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