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

\( 32 q - 3 q^{2} - q^{4} - 6 q^{5} + 21 q^{6} + 6 q^{9} + O(q^{10}) \)

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