Space of Modular Forms of Level 28, Weight 3, and Character 28.b

• Label: 28.3.b
• Level: 28
• Weight: 3
• Character orbit: b
• Rep. character: \(\chi_{28}(13,\cdot)\)
• Character field: \(\Q\)
• Dimension: 2
• Newforms: 1
• Sturm bound: 12
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Character orbit:	\([\chi]\)	=	28.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 7 \)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(28, [\chi])\).

	Total	New	Old
Modular forms	11	2	9
Cusp forms	5	2	3
Eisenstein series	6	0	6

Trace form

\( 2q + 10q^{7} - 30q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) into irreducible Hecke orbits

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
28.3.b.a	\(2\)	\(0.763\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(10\)	\(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)