Space of modular forms of level 133, weight 2, and Character 133.p

• Label: 133.2.p
• Level: $133$
• Weight: $2$
• Character orbit: 133.p
• Rep. character: $\chi_{133}(27,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $26$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(26\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(133, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

\( 20 q - 6 q^{2} + 2 q^{4} + 4 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(133, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
133.2.p.a	$133$	$2$	133.p	133.p	$6$	$4$	$2$	$1.062$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(-3\)	\(-2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
133.2.p.b	$133$	$2$	133.p	133.p	$6$	$4$	$2$	$1.062$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(-3\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
133.2.p.c	$133$	$2$	133.p	133.p	$6$	$12$	$6$	$1.062$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}+\beta _{6}+\beta _{11})q^{2}+(-\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots\)