Space of Modular Forms of Level 36, Weight 2, and Character 36.b

• Label: 36.2.b
• Level: 36
• Weight: 2
• Character orbit: b
• Rep. character: \(\chi_{36}(35,\cdot)\)
• Character field: \(\Q\)
• Dimension: 2
• Newforms: 1
• Sturm bound: 12
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	36.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 12 \)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	2	2	0
Eisenstein series	8	0	8

Trace form

\( 2q - 4q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into irreducible Hecke orbits

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
36.2.b.a	\(2\)	\(0.287\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\)