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

• Label: 637.2.q
• Level: $637$
• Weight: $2$
• Character orbit: 637.q
• Rep. character: $\chi_{637}(491,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $86$
• Newform subspaces: $10$
• Sturm bound: $130$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(130\)
Trace bound:			\(3\)
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	106	42
Cusp forms	116	86	30
Eisenstein series	32	20	12

Trace form

\( 86 q + 3 q^{2} + 2 q^{3} + 39 q^{4} + 12 q^{6} - 35 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
637.2.q.a	$637$	$2$	637.q	13.e	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					13.2.e.a	$2$	$0$	\(-3\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.b	$637$	$2$	637.q	13.e	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.k.a	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.c	$637$	$2$	637.q	13.e	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.k.a	$2$	$0$	\(3\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.d	$637$	$2$	637.q	13.e	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-13})\)	None		✓			637.2.q.d	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
637.2.q.e	$637$	$2$	637.q	13.e	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			637.2.q.e	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.q.f	$637$	$2$	637.q	13.e	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			637.2.q.e	$2$	$0$	\(3\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.q.g	$637$	$2$	637.q	13.e	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.k.b	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{10}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.h	$637$	$2$	637.q	13.e	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.q.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.q.i	$637$	$2$	637.q	13.e	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.k.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.j	$637$	$2$	637.q	13.e	$6$	$32$	$16$	$5.086$		None		✓	✓		637.2.q.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)