Space of modular forms of level 153, weight 4, and Character 153.n

• Label: 153.4.n
• Level: $153$
• Weight: $4$
• Character orbit: 153.n
• Rep. character: $\chi_{153}(4,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $208$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 153 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(153, [\chi])\).

	Total	New	Old
Modular forms	224	224	0
Cusp forms	208	208	0
Eisenstein series	16	16	0

Trace form

\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(153, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
153.4.n.a	$153$	$4$	153.n	153.n	$12$	$208$	$52$	$9.027$		None		$4$	$0$	\(0\)	\(-6\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$