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

• Label: 133.2.c
• Level: $133$
• Weight: $2$
• Character orbit: 133.c
• Rep. character: $\chi_{133}(132,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $26$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q\)
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	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

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

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.c.a	$133$	$2$	133.c	133.c	$2$	$2$	$2$	$1.062$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{4}+(-1+2\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
133.2.c.b	$133$	$2$	133.c	133.c	$2$	$4$	$4$	$1.062$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
133.2.c.c	$133$	$2$	133.c	133.c	$2$	$4$	$4$	$1.062$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)