Space of modular forms of level 16, weight 6, and trivial character

• Label: 16.6.a
• Level: $16$
• Weight: $6$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(16))\).

	Total	New	Old
Modular forms	13	3	10
Cusp forms	7	2	5
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
\(+\)		\(6\)	\(1\)	\(5\)		\(3\)	\(1\)	\(2\)		\(3\)	\(0\)	\(3\)
\(-\)		\(7\)	\(2\)	\(5\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)

Trace form

2 * q - 8 * q^3 - 20 * q^5 + 112 * q^7 + 58 * q^9 - 664 * q^11 + 60 * q^13 + 2128 * q^15 - 604 * q^17 - 3880 * q^19 + 576 * q^21 + 3920 * q^23 + 2142 * q^25 - 2384 * q^27 - 3876 * q^29 + 1472 * q^31 - 4000 * q^33 + 2976 * q^35 + 10028 * q^37 - 14576 * q^39 + 8340 * q^41 + 21288 * q^43 - 16964 * q^45 - 22368 * q^47 - 25294 * q^49 + 31088 * q^51 + 31180 * q^53 - 19984 * q^55 + 50848 * q^57 - 9208 * q^59 - 53220 * q^61 - 4944 * q^63 - 57944 * q^65 - 6280 * q^67 + 52928 * q^69 + 78832 * q^71 + 62676 * q^73 - 49528 * q^75 - 50496 * q^77 + 32352 * q^79 - 97742 * q^81 - 135080 * q^83 + 120728 * q^85 + 58512 * q^87 + 101748 * q^89 - 25312 * q^91 - 165632 * q^93 + 180112 * q^95 - 73532 * q^97 + 33992 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.6.a.a	$16$	$6$	16.a	1.a	$1$	$1$	$1$	$2.566$	\(\Q\)	None	✓		✓	✓	8.6.a.a	$1$	$1$	\(0\)	\(-20\)	\(-74\)	\(24\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b	$16$	$6$	16.a	1.a	$1$	$1$	$1$	$2.566$	\(\Q\)	None	✓		✓	✓	4.6.a.a	$1$	$0$	\(0\)	\(12\)	\(54\)	\(88\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(16)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)