Space of modular forms of level 16, weight 4, and trivial character

• Label: 16.4.a
• Level: $16$
• Weight: $4$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(16))\).

	Total	New	Old
Modular forms	9	2	7
Cusp forms	3	1	2
Eisenstein series	6	1	5

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

\(2\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(5\)	\(1\)	\(4\)		\(2\)	\(1\)	\(1\)		\(3\)	\(0\)	\(3\)
\(-\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)		\(3\)	\(1\)	\(2\)

Trace form

q + 4 * q^3 - 2 * q^5 - 24 * q^7 - 11 * q^9 + 44 * q^11 + 22 * q^13 - 8 * q^15 + 50 * q^17 - 44 * q^19 - 96 * q^21 + 56 * q^23 - 121 * q^25 - 152 * q^27 + 198 * q^29 + 160 * q^31 + 176 * q^33 + 48 * q^35 - 162 * q^37 + 88 * q^39 - 198 * q^41 - 52 * q^43 + 22 * q^45 - 528 * q^47 + 233 * q^49 + 200 * q^51 - 242 * q^53 - 88 * q^55 - 176 * q^57 + 668 * q^59 + 550 * q^61 + 264 * q^63 - 44 * q^65 - 188 * q^67 + 224 * q^69 - 728 * q^71 + 154 * q^73 - 484 * q^75 - 1056 * q^77 + 656 * q^79 - 311 * q^81 - 236 * q^83 - 100 * q^85 + 792 * q^87 + 714 * q^89 - 528 * q^91 + 640 * q^93 + 88 * q^95 - 478 * q^97 - 484 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
16.4.a.a	$16$	$4$	16.a	1.a	$1$	$1$	$1$	$0.944$	\(\Q\)	None	✓		✓	✓	8.4.a.a	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-24\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(16)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)