Space of modular forms of level 36, weight 4, and Character 36.e

• Label: 36.4.e
• Level: $36$
• Weight: $4$
• Character orbit: 36.e
• Rep. character: $\chi_{36}(13,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(36, [\chi])\).

	Total	New	Old
Modular forms	42	6	36
Cusp forms	30	6	24
Eisenstein series	12	0	12

Trace form

6 * q - 3 * q^3 + 6 * q^5 - 6 * q^7 + 39 * q^9 + 51 * q^11 + 12 * q^13 - 180 * q^15 - 222 * q^17 + 30 * q^19 - 120 * q^21 + 210 * q^23 - 3 * q^25 + 648 * q^27 + 456 * q^29 + 48 * q^31 - 603 * q^33 - 1104 * q^35 - 96 * q^37 - 36 * q^39 + 897 * q^41 + 129 * q^43 + 1494 * q^45 + 522 * q^47 - 225 * q^49 - 1647 * q^51 - 2208 * q^53 - 216 * q^55 - 645 * q^57 + 453 * q^59 - 402 * q^61 + 1896 * q^63 + 1110 * q^65 - 213 * q^67 - 198 * q^69 + 120 * q^71 + 750 * q^73 + 921 * q^75 + 1128 * q^77 + 552 * q^79 - 549 * q^81 - 612 * q^83 + 1188 * q^85 - 1386 * q^87 - 924 * q^89 - 264 * q^91 - 1998 * q^93 - 2184 * q^95 + 93 * q^97 - 1854 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(36, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.4.e.a	$36$	$4$	36.e	9.c	$3$	$6$	$3$	$2.124$	6.0.6831243.2	None		✓	✓	✓	36.4.e.a	$2$	$0$	\(0\)	\(-3\)	\(6\)	\(-6\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(1-3\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)