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

• Label: 637.2.e
• Level: $637$
• Weight: $2$
• Character orbit: 637.e
• Rep. character: $\chi_{637}(79,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $15$
• Sturm bound: $130$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(130\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	148	80	68
Cusp forms	116	80	36
Eisenstein series	32	0	32

Trace form

80 * q + 4 * q^2 - 36 * q^4 + 2 * q^5 - 12 * q^8 - 44 * q^9 - 10 * q^10 + 6 * q^11 - 10 * q^12 - 4 * q^13 + 20 * q^15 - 12 * q^16 - 4 * q^17 + 10 * q^18 + 8 * q^19 - 32 * q^20 - 68 * q^22 - 2 * q^23 + 20 * q^24 - 34 * q^25 + 6 * q^26 - 4 * q^29 + 30 * q^30 + 4 * q^31 + 46 * q^32 + 8 * q^33 + 32 * q^34 + 4 * q^36 + 24 * q^37 - 26 * q^38 + 8 * q^40 - 28 * q^41 + 12 * q^43 + 18 * q^44 - 32 * q^45 + 52 * q^46 + 2 * q^47 + 76 * q^48 - 76 * q^50 - 20 * q^51 + 6 * q^52 + 26 * q^53 + 18 * q^54 - 30 * q^58 + 10 * q^59 - 24 * q^60 - 12 * q^61 + 76 * q^62 - 28 * q^64 + 4 * q^65 + 6 * q^66 + 24 * q^67 - 18 * q^68 - 56 * q^69 - 60 * q^71 + 28 * q^72 + 22 * q^73 - 10 * q^74 - 20 * q^75 - 48 * q^76 + 20 * q^78 + 34 * q^79 + 70 * q^80 - 72 * q^81 + 44 * q^82 - 12 * q^83 - 60 * q^85 + 14 * q^86 - 28 * q^87 - 4 * q^89 + 88 * q^90 + 140 * q^92 + 66 * q^93 + 46 * q^94 + 22 * q^95 - 22 * q^96 + 68 * q^97 + 72 * q^99

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.e.a	$637$	$2$	637.e	7.c	$3$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
637.2.e.b	$637$	$2$	637.e	7.c	$3$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.a.b	$2$	$0$	\(0\)	\(-2\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.c	$637$	$2$	637.e	7.c	$3$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.a.b	$2$	$0$	\(0\)	\(2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.d	$637$	$2$	637.e	7.c	$3$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.a.a	$2$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.e	$637$	$2$	637.e	7.c	$3$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.a.a	$2$	$0$	\(2\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.f	$637$	$2$	637.e	7.c	$3$	$4$	$2$	$5.086$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					91.2.a.c	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.g	$637$	$2$	637.e	7.c	$3$	$4$	$2$	$5.086$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					91.2.a.c	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.h	$637$	$2$	637.e	7.c	$3$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					91.2.e.b	$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3})q^{2}+(2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.e.i	$637$	$2$	637.e	7.c	$3$	$6$	$3$	$5.086$	6.0.2696112.1	None					91.2.a.d	$2$	$0$	\(-1\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
637.2.e.j	$637$	$2$	637.e	7.c	$3$	$6$	$3$	$5.086$	6.0.2696112.1	None					91.2.a.d	$2$	$0$	\(-1\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
637.2.e.k	$637$	$2$	637.e	7.c	$3$	$6$	$3$	$5.086$	6.0.4406832.1	None		✓			637.2.a.h	$2$	$0$	\(2\)	\(-4\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.l	$637$	$2$	637.e	7.c	$3$	$6$	$3$	$5.086$	6.0.4406832.1	None		✓			637.2.a.h	$2$	$0$	\(2\)	\(4\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.m	$637$	$2$	637.e	7.c	$3$	$10$	$5$	$5.086$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					91.2.e.c	$2$	$0$	\(-4\)	\(0\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
637.2.e.n	$637$	$2$	637.e	7.c	$3$	$12$	$6$	$5.086$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			637.2.a.m	$2$	$0$	\(0\)	\(-8\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{11})q^{2}+(\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.e.o	$637$	$2$	637.e	7.c	$3$	$12$	$6$	$5.086$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			637.2.a.m	$2$	$0$	\(0\)	\(8\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{8}+\cdots)q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)