Space of modular forms of level 637, weight 2, and Character 637.r

• Label: 637.2.r
• Level: $637$
• Weight: $2$
• Character orbit: 637.r
• Rep. character: $\chi_{637}(116,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $84$
• Newform subspaces: $7$
• Sturm bound: $130$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(130\)
Trace bound:			\(12\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

	Total	New	Old
Modular forms	148	100	48
Cusp forms	116	84	32
Eisenstein series	32	16	16

Trace form

\( 84 q + 4 q^{3} + 38 q^{4} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
637.2.r.a	$637$	$2$	637.r	91.r	$6$	$4$	$2$	$5.086$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}-2\zeta_{12}^{2}q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
637.2.r.b	$637$	$2$	637.r	91.r	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-13})\)	\(\Q(\sqrt{-91}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-2\beta _{2}q^{4}-\beta _{1}q^{5}+(3-3\beta _{2})q^{9}+\beta _{3}q^{13}+\cdots\)
637.2.r.c	$637$	$2$	637.r	91.r	$6$	$4$	$2$	$5.086$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
637.2.r.d	$637$	$2$	637.r	91.r	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{2}+\beta _{11}q^{3}+\cdots\)
637.2.r.e	$637$	$2$	637.r	91.r	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{2}-\beta _{11}q^{3}+\cdots\)
637.2.r.f	$637$	$2$	637.r	91.r	$6$	$16$	$8$	$5.086$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{8})q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+\cdots\)
637.2.r.g	$637$	$2$	637.r	91.r	$6$	$32$	$16$	$5.086$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)