Space of modular forms of level 106, weight 2, and Character 106.e

• Label: 106.2.e
• Level: $106$
• Weight: $2$
• Character orbit: 106.e
• Rep. character: $\chi_{106}(7,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 106 = 2 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	106.e (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(106, [\chi])\).

	Total	New	Old
Modular forms	192	48	144
Cusp forms	144	48	96
Eisenstein series	48	0	48

Trace form

\( 48 q + 4 q^{4} - 2 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(106, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
106.2.e.a	$106$	$2$	106.e	53.e	$26$	$48$	$4$	$0.846$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{26}]$

Decomposition of \(S_{2}^{\mathrm{old}}(106, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(106, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 2}\)