Space of modular forms of level 28, weight 4, and trivial character

• Label: 28.4.a
• Level: $28$
• Weight: $4$
• Character orbit: 28.a
• Rep. character: $\chi_{28}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(28))\).

	Total	New	Old
Modular forms	15	2	13
Cusp forms	9	2	7
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(1\)

Trace form

\( 2 q - 6 q^{3} - 2 q^{5} + 62 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(28))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
28.4.a.a	$28$	$4$	28.a	1.a	$1$	$1$	$1$	$1.652$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-10\)	\(-8\)	\(-7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-10q^{3}-8q^{5}-7q^{7}+73q^{9}-40q^{11}+\cdots\)
28.4.a.b	$28$	$4$	28.a	1.a	$1$	$1$	$1$	$1.652$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(6\)	\(7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}+6q^{5}+7q^{7}-11q^{9}-12q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(28))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(28)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)