Space of modular forms of level 152, weight 4, and Character 152.i

• Label: 152.4.i
• Level: $152$
• Weight: $4$
• Character orbit: 152.i
• Rep. character: $\chi_{152}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $30$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(152, [\chi])\).

	Total	New	Old
Modular forms	128	30	98
Cusp forms	112	30	82
Eisenstein series	16	0	16

Trace form

\( 30 q + 5 q^{3} - 36 q^{7} - 150 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.4.i.a	$152$	$4$	152.i	19.c	$3$	$14$	$7$	$8.968$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(5\)	\(5\)	\(-28\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
152.4.i.b	$152$	$4$	152.i	19.c	$3$	$16$	$8$	$8.968$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-8\)	$2^{12}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)