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

• Label: 637.2.k
• Level: $637$
• Weight: $2$
• Character orbit: 637.k
• Rep. character: $\chi_{637}(459,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $86$
• Newform subspaces: $10$
• Sturm bound: $130$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(130\)
Trace bound:			\(5\)
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	146	102	44
Cusp forms	114	86	28
Eisenstein series	32	16	16

Trace form

86 * q + 2 * q^3 - 78 * q^4 + 6 * q^6 - 41 * q^9 - 9 * q^10 - 3 * q^11 + 2 * q^12 + 4 * q^13 - 15 * q^15 + 58 * q^16 + 22 * q^17 + 51 * q^18 - 6 * q^19 + 6 * q^20 + 10 * q^23 - 18 * q^24 + 35 * q^25 - 6 * q^26 - 22 * q^27 - 2 * q^29 + 26 * q^30 - 15 * q^31 + 15 * q^33 + 37 * q^36 - 16 * q^38 - 21 * q^39 + 4 * q^40 + 15 * q^41 - 22 * q^43 - 48 * q^44 - 14 * q^48 + 30 * q^50 - 36 * q^51 + 5 * q^52 + 17 * q^53 + 24 * q^55 + 111 * q^58 + 129 * q^60 + 2 * q^61 - 38 * q^62 - 16 * q^64 - 70 * q^65 + 43 * q^66 - 54 * q^67 - 10 * q^68 - 7 * q^69 - 75 * q^71 - 159 * q^72 - 57 * q^73 - 6 * q^74 + 6 * q^75 + 42 * q^76 - 123 * q^78 + 6 * q^79 + 78 * q^80 - 23 * q^81 + 4 * q^82 - 9 * q^85 + 114 * q^86 + 26 * q^87 + 29 * q^88 + 12 * q^90 + 62 * q^92 + 14 * q^94 - 70 * q^95 - 12 * q^96 + 12 * q^97

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.k.a	$637$	$2$	637.k	91.k	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					13.2.e.a	$2$	$1$	\(0\)	\(-2\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}-2\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.b	$637$	$2$	637.k	91.k	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					91.2.k.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}-\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.c	$637$	$2$	637.k	91.k	$6$	$2$	$1$	$5.086$	\(\Q(\sqrt{-3}) \)	None					13.2.e.a	$2$	$0$	\(0\)	\(2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}+2\zeta_{6}q^{3}-q^{4}+(2+\cdots)q^{5}+\cdots\)
637.2.k.d	$637$	$2$	637.k	91.k	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			637.2.q.e	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.k.e	$637$	$2$	637.k	91.k	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-13})\)	None		✓			637.2.q.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\beta _{2})q^{2}-q^{4}+\beta _{1}q^{5}+(1-2\beta _{2}+\cdots)q^{8}+\cdots\)
637.2.k.f	$637$	$2$	637.k	91.k	$6$	$4$	$2$	$5.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			637.2.q.e	$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
637.2.k.g	$637$	$2$	637.k	91.k	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{8})q^{2}+(\beta _{2}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.h	$637$	$2$	637.k	91.k	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.q.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{8})q^{2}+(-\beta _{2}-\beta _{9})q^{3}+\cdots\)
637.2.k.i	$637$	$2$	637.k	91.k	$6$	$12$	$6$	$5.086$	12.0.\(\cdots\).1	None					91.2.k.b	$2$	$0$	\(0\)	\(3\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.j	$637$	$2$	637.k	91.k	$6$	$32$	$16$	$5.086$		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

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