Space of modular forms of level 154, weight 4, and Character 154.n

• Label: 154.4.n
• Level: $154$
• Weight: $4$
• Character orbit: 154.n
• Rep. character: $\chi_{154}(17,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $192$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	154.n (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(154, [\chi])\).

	Total	New	Old
Modular forms	608	192	416
Cusp forms	544	192	352
Eisenstein series	64	0	64

Trace form

\( 192 q - 96 q^{4} - 48 q^{5} - 20 q^{7} - 312 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(154, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
154.4.n.a	$154$	$4$	154.n	77.n	$30$	$192$	$24$	$9.086$		None		$4$	$0$	\(0\)	\(0\)	\(-48\)	\(-20\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{4}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(154, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)