Space of modular forms of level 58, weight 8, and Character 58.e

• Label: 58.8.e
• Level: $58$
• Weight: $8$
• Character orbit: 58.e
• Rep. character: $\chi_{58}(5,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	58.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(58, [\chi])\).

	Total	New	Old
Modular forms	324	108	216
Cusp forms	300	108	192
Eisenstein series	24	0	24

Trace form

\( 108 q + 1152 q^{4} + 82 q^{5} - 1888 q^{6} + 1348 q^{7} + 15368 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(58, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
58.8.e.a	$58$	$8$	58.e	29.e	$14$	$108$	$18$	$18.118$		None		✓	58.8.e.a	$2$	$0$	\(0\)	\(0\)	\(82\)	\(1348\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{8}^{\mathrm{old}}(58, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(58, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)