Space of modular forms of level 36, weight 6, and Character 36.e

• Label: 36.6.e
• Level: $36$
• Weight: $6$
• Character orbit: 36.e
• Rep. character: $\chi_{36}(13,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(36, [\chi])\).

	Total	New	Old
Modular forms	66	10	56
Cusp forms	54	10	44
Eisenstein series	12	0	12

Trace form

10 * q + 12 * q^3 - 21 * q^5 + 29 * q^7 + 12 * q^9 + 177 * q^11 - 181 * q^13 + 117 * q^15 + 2280 * q^17 - 832 * q^19 - 207 * q^21 + 399 * q^23 - 4778 * q^25 - 7128 * q^27 - 6033 * q^29 + 2759 * q^31 + 9603 * q^33 + 37146 * q^35 - 15172 * q^37 + 5529 * q^39 - 18435 * q^41 + 1469 * q^43 - 64089 * q^45 - 25155 * q^47 - 4056 * q^49 + 90612 * q^51 + 116844 * q^53 + 14778 * q^55 + 26934 * q^57 - 90537 * q^59 + 1403 * q^61 - 198255 * q^63 - 148407 * q^65 + 13907 * q^67 + 214425 * q^69 + 229368 * q^71 + 15200 * q^73 + 44640 * q^75 - 211983 * q^77 + 29993 * q^79 - 404172 * q^81 - 228951 * q^83 - 49662 * q^85 + 397323 * q^87 + 598332 * q^89 + 124930 * q^91 + 250041 * q^93 - 394764 * q^95 + 40541 * q^97 - 697239 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(36, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.6.e.a	$36$	$6$	36.e	9.c	$3$	$10$	$5$	$5.774$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	36.6.e.a	$2$	$0$	\(0\)	\(12\)	\(-21\)	\(29\)	$2^{8}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)