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

• Label: 153.4.l
• Level: $153$
• Weight: $4$
• Character orbit: 153.l
• Rep. character: $\chi_{153}(19,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $84$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	232	92	140
Cusp forms	200	84	116
Eisenstein series	32	8	24

Trace form

\( 84 q + 4 q^{2} - 12 q^{5} - 4 q^{7} - 28 q^{8} + O(q^{10}) \)

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.l.a	$153$	$4$	153.l	17.d	$8$	$12$	$3$	$9.027$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(4\)	\(0\)	\(20\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{2}-\beta _{11})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
153.4.l.b	$153$	$4$	153.l	17.d	$8$	$32$	$8$	$9.027$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
153.4.l.c	$153$	$4$	153.l	17.d	$8$	$40$	$10$	$9.027$		None		$2$	$0$	\(0\)	\(0\)	\(-32\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{4}^{\mathrm{old}}(153, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(153, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)