Space of modular forms of level 608, weight 4, and Character 608.b

• Label: 608.4.b
• Level: $608$
• Weight: $4$
• Character orbit: 608.b
• Rep. character: $\chi_{608}(303,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$608 = 2^{5} \cdot 19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	608.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$152$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$320$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(608, [\chi])$.

	Total	New	Old
Modular forms	248	62	186
Cusp forms	232	58	174
Eisenstein series	16	4	12

Trace form

$58 q - 490 q^{9} + 4 q^{11} - 4 q^{17} - 22 q^{19} - 1254 q^{25} - 40 q^{35} + 4 q^{43} - 2978 q^{49} - 288 q^{57} + 428 q^{73} + 2586 q^{81} - 2676 q^{83} + 5468 q^{99}+O(q^{100})$

Decomposition of $S_{4}^{\mathrm{new}}(608, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
608.4.b.a	$608$	$4$	608.b	152.b	$2$	$2$	$2$	$35.873$	$\Q(\sqrt{-2})$	$\Q(\sqrt{-2})$					152.4.b.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{3}+19q^{9}-18q^{11}+90q^{17}+\cdots$
608.4.b.b	$608$	$4$	608.b	152.b	$2$	$56$	$56$	$35.873$		None			✓		152.4.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{4}^{\mathrm{old}}(608, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(608, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(152, [\chi])$$^{\oplus 3}$