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

• Label: 36.4.b
• Level: $36$
• Weight: $4$
• Character orbit: 36.b
• Rep. character: $\chi_{36}(35,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
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	22	6	16
Cusp forms	14	6	8
Eisenstein series	8	0	8

Trace form

\( 6 q + 12 q^{4} + O(q^{10}) \)

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.b.a	$36$	$4$	36.b	12.b	$2$	$2$	$2$	$2.124$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{2}-8q^{4}+13\beta q^{5}-2^{4}\beta q^{8}+\cdots\)
36.4.b.b	$36$	$4$	36.b	12.b	$2$	$4$	$4$	$2.124$	\(\Q(\sqrt{-2}, \sqrt{-15})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(7-\beta _{3})q^{4}-7\beta _{2}q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(36, [\chi]) \cong \)