Space of modular forms of level 134, weight 2, and Character 134.g

• Label: 134.2.g
• Level: $134$
• Weight: $2$
• Character orbit: 134.g
• Rep. character: $\chi_{134}(17,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $100$
• Newform subspaces: $2$
• Sturm bound: $34$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.g (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{33})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(34\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(134, [\chi])\).

	Total	New	Old
Modular forms	380	100	280
Cusp forms	300	100	200
Eisenstein series	80	0	80

Trace form

\( 100 q + q^{2} - 6 q^{3} + 5 q^{4} - 3 q^{6} - 2 q^{7} - 2 q^{8} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
134.2.g.a	$134$	$2$	134.g	67.g	$33$	$40$	$2$	$1.070$		None		$2$	$0$	\(-2\)	\(-6\)	\(0\)	\(1\)		$\mathrm{SU}(2)[C_{33}]$
134.2.g.b	$134$	$2$	134.g	67.g	$33$	$60$	$3$	$1.070$		None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{33}]$

Decomposition of \(S_{2}^{\mathrm{old}}(134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)