Space of modular forms of level 36, weight 8, and Character 36.e

• Label: 36.8.e
• Level: $36$
• Weight: $8$
• Character orbit: 36.e
• Rep. character: $\chi_{36}(13,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	36.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(36, [\chi])\).

	Total	New	Old
Modular forms	90	14	76
Cusp forms	78	14	64
Eisenstein series	12	0	12

Trace form

14 * q + 321 * q^5 - 83 * q^7 + 264 * q^9 - 111 * q^11 - 1847 * q^13 - 7875 * q^15 - 96 * q^17 + 20248 * q^19 + 9003 * q^21 + 19119 * q^23 - 73378 * q^25 + 158760 * q^27 + 6045 * q^29 - 153089 * q^31 - 332487 * q^33 + 27426 * q^35 + 139348 * q^37 + 76641 * q^39 + 446631 * q^41 - 384347 * q^43 + 996309 * q^45 + 298413 * q^47 - 351876 * q^49 - 967464 * q^51 - 908076 * q^53 - 2526966 * q^55 + 12150 * q^57 + 2619543 * q^59 - 146231 * q^61 + 4217721 * q^63 + 2535735 * q^65 + 1637419 * q^67 - 3024117 * q^69 - 8706984 * q^71 - 4264520 * q^73 - 4432044 * q^75 + 9785451 * q^77 + 2402185 * q^79 + 16357320 * q^81 + 12936357 * q^83 - 1015002 * q^85 - 24976413 * q^87 - 39369660 * q^89 - 984406 * q^91 - 4054125 * q^93 + 22685196 * q^95 - 2853257 * q^97 + 69035013 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(36, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.8.e.a	$36$	$8$	36.e	9.c	$3$	$14$	$7$	$11.246$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓	✓	36.8.e.a	$2$	$0$	\(0\)	\(0\)	\(321\)	\(-83\)	$2^{20}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-4\beta _{2}-\beta _{4})q^{3}+(\beta _{1}-46\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)