Space of modular forms of level 726, weight 2, and Character 726.e

• Label: 726.2.e
• Level: $726$
• Weight: $2$
• Character orbit: 726.e
• Rep. character: $\chi_{726}(487,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $72$
• Newform subspaces: $18$
• Sturm bound: $264$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(264\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(726, [\chi])\).

	Total	New	Old
Modular forms	624	72	552
Cusp forms	432	72	360
Eisenstein series	192	0	192

Trace form

72 * q - 18 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 - 18 * q^9 + 12 * q^10 + 4 * q^14 - 2 * q^15 - 18 * q^16 + 16 * q^17 - 20 * q^19 - 8 * q^20 + 16 * q^21 + 16 * q^23 - 2 * q^24 - 6 * q^25 - 16 * q^26 - 2 * q^28 + 12 * q^29 - 12 * q^30 - 6 * q^31 + 24 * q^34 - 28 * q^35 - 18 * q^36 - 28 * q^37 - 16 * q^38 - 8 * q^39 + 2 * q^40 - 20 * q^41 - 2 * q^42 + 32 * q^43 - 8 * q^45 - 12 * q^46 - 46 * q^49 + 24 * q^50 + 12 * q^51 + 4 * q^53 + 8 * q^54 - 16 * q^56 + 12 * q^57 - 18 * q^58 + 4 * q^59 + 8 * q^60 + 4 * q^61 + 12 * q^62 + 8 * q^63 - 18 * q^64 + 8 * q^65 + 64 * q^67 + 16 * q^68 - 12 * q^69 + 14 * q^70 + 6 * q^73 + 16 * q^74 - 32 * q^75 + 20 * q^79 + 12 * q^80 - 18 * q^81 - 24 * q^82 - 28 * q^83 - 4 * q^84 + 24 * q^85 + 12 * q^86 - 20 * q^87 + 32 * q^89 - 8 * q^90 + 40 * q^91 - 24 * q^92 + 60 * q^93 - 16 * q^94 - 52 * q^95 - 2 * q^96 + 44 * q^97 - 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(726, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
726.2.e.a	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.b	$2$	$0$	\(-1\)	\(-1\)	\(-5\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.b	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.a	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.c	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.b	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.d	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.e	$4$	$0$	\(-1\)	\(-1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.e	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.c	$4$	$0$	\(-1\)	\(-1\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.f	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.a	$2$	$0$	\(-1\)	\(1\)	\(-7\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.g	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.b	$4$	$0$	\(-1\)	\(1\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.h	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.b	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.i	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.a	$4$	$0$	\(-1\)	\(1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.j	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.b	$2$	$0$	\(1\)	\(-1\)	\(-5\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.k	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.a	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.l	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.e	$4$	$0$	\(1\)	\(-1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.m	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.c	$4$	$0$	\(1\)	\(-1\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.n	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.a	$2$	$0$	\(1\)	\(1\)	\(-7\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.o	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.a.b	$4$	$0$	\(1\)	\(1\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.p	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.b	$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.q	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None		✓			726.2.a.a	$4$	$0$	\(1\)	\(1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.r	$726$	$2$	726.e	11.c	$5$	$4$	$1$	$5.797$	\(\Q(\zeta_{10})\)	None					66.2.e.a	$2$	$0$	\(1\)	\(1\)	\(8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(726, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(726, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)