Space of modular forms of level 152, weight 7, and Character 152.e

• Label: 152.7.e
• Level: $152$
• Weight: $7$
• Character orbit: 152.e
• Rep. character: $\chi_{152}(113,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $1$
• Sturm bound: $140$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	152.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(140\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(152, [\chi])\).

	Total	New	Old
Modular forms	124	30	94
Cusp forms	116	30	86
Eisenstein series	8	0	8

Trace form

\( 30 q - 720 q^{7} - 8670 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.7.e.a	$152$	$7$	152.e	19.b	$2$	$30$	$30$	$34.968$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-720\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(152, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)