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

• Label: 36.6.b
• Level: $36$
• Weight: $6$
• Character orbit: 36.b
• Rep. character: $\chi_{36}(35,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	34	10	24
Cusp forms	26	10	16
Eisenstein series	8	0	8

Trace form

\( 10 q - 20 q^{4} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.6.b.a	$36$	$6$	36.b	12.b	$2$	$2$	$2$	$5.774$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4\beta q^{2}-2^{5}q^{4}-79\beta q^{5}-2^{7}\beta q^{8}+\cdots\)
36.6.b.b	$36$	$6$	36.b	12.b	$2$	$8$	$8$	$5.774$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(6+\beta _{7})q^{4}+(6\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(36, [\chi]) \cong \)