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

• Label: 608.3.g
• Level: $608$
• Weight: $3$
• Character orbit: 608.g
• Rep. character: $\chi_{608}(113,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	608.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	168	42	126
Cusp forms	152	38	114
Eisenstein series	16	4	12

Trace form

\( 38 q + 4 q^{7} + 98 q^{9} - 4 q^{17} + 4 q^{23} - 154 q^{25} + 40 q^{39} + 196 q^{47} + 210 q^{49} - 96 q^{55} - 108 q^{57} + 236 q^{63} + 156 q^{73} + 270 q^{81} - 408 q^{87} + 304 q^{95}+O(q^{100}) \)

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.g.a	$608$	$3$	608.g	152.g	$2$	$3$	$3$	$16.567$	3.3.4104.1	\(\Q(\sqrt{-38}) \)	✓				152.3.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{7}+(9-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
608.3.g.b	$608$	$3$	608.g	152.g	$2$	$3$	$3$	$16.567$	3.3.4104.1	\(\Q(\sqrt{-38}) \)	✓				152.3.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{7}+(9-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
608.3.g.c	$608$	$3$	608.g	152.g	$2$	$32$	$32$	$16.567$		None			✓		152.3.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$

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

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