Space of modular forms of level 627, weight 2, and Character 627.h

• Label: 627.2.h
• Level: $627$
• Weight: $2$
• Character orbit: 627.h
• Rep. character: $\chi_{627}(208,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(627, [\chi])\).

	Total	New	Old
Modular forms	84	40	44
Cusp forms	76	40	36
Eisenstein series	8	0	8

Trace form

\( 40 q + 40 q^{4} - 4 q^{5} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(627, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
627.2.h.a	$627$	$2$	627.h	209.d	$2$	$16$	$16$	$5.007$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}-\beta _{12}q^{3}+(1+\beta _{10}-\beta _{15})q^{4}+\cdots\)
627.2.h.b	$627$	$2$	627.h	209.d	$2$	$24$	$24$	$5.007$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(627, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(627, [\chi]) \cong \)