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

• Label: 36.4.h
• Level: $36$
• Weight: $4$
• Character orbit: 36.h
• Rep. character: $\chi_{36}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

32 * q - 3 * q^2 - q^4 - 6 * q^5 + 21 * q^6 + 6 * q^9 - 20 * q^10 - 6 * q^12 - 2 * q^13 - 78 * q^14 - q^16 - 120 * q^18 - 234 * q^20 - 126 * q^21 + 15 * q^22 + 3 * q^24 + 198 * q^25 - 132 * q^28 + 78 * q^29 + 438 * q^30 + 687 * q^32 - 396 * q^33 - 191 * q^34 + 1023 * q^36 - 8 * q^37 + 891 * q^38 + 34 * q^40 - 156 * q^41 + 732 * q^42 - 306 * q^45 + 48 * q^46 - 1371 * q^48 + 194 * q^49 - 1977 * q^50 - 332 * q^52 - 3021 * q^54 - 3006 * q^56 + 402 * q^57 - 314 * q^58 - 1302 * q^60 - 2 * q^61 + 410 * q^64 + 690 * q^65 + 3114 * q^66 + 4845 * q^68 + 210 * q^69 + 84 * q^70 + 5475 * q^72 - 836 * q^73 + 5874 * q^74 - 495 * q^76 + 978 * q^77 + 2484 * q^78 + 2382 * q^81 + 682 * q^82 - 5850 * q^84 + 248 * q^85 - 8331 * q^86 + 531 * q^88 - 11202 * q^90 - 8724 * q^92 + 222 * q^93 + 168 * q^94 - 3900 * q^96 + 16 * q^97

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.h.a	$36$	$4$	36.h	36.h	$6$	$8$	$4$	$2.124$	8.0.\(\cdots\).1	None		✓			36.4.h.a	$4$	$0$	\(-3\)	\(0\)	\(66\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(2\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
36.4.h.b	$36$	$4$	36.h	36.h	$6$	$24$	$12$	$2.124$		None		✓	✓		36.4.h.b	$4$	$0$	\(0\)	\(0\)	\(-72\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$