Space of modular forms of level 6, weight 4, and trivial character

• Label: 6.4.a
• Level: $6$
• Weight: $4$
• Character orbit: 6.a
• Rep. character: $\chi_{6}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(6))\).

	Total	New	Old
Modular forms	5	1	4
Cusp forms	1	1	0
Eisenstein series	4	0	4

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

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(0\)

Trace form

q - 2 * q^2 - 3 * q^3 + 4 * q^4 + 6 * q^5 + 6 * q^6 - 16 * q^7 - 8 * q^8 + 9 * q^9 - 12 * q^10 + 12 * q^11 - 12 * q^12 + 38 * q^13 + 32 * q^14 - 18 * q^15 + 16 * q^16 - 126 * q^17 - 18 * q^18 + 20 * q^19 + 24 * q^20 + 48 * q^21 - 24 * q^22 + 168 * q^23 + 24 * q^24 - 89 * q^25 - 76 * q^26 - 27 * q^27 - 64 * q^28 + 30 * q^29 + 36 * q^30 - 88 * q^31 - 32 * q^32 - 36 * q^33 + 252 * q^34 - 96 * q^35 + 36 * q^36 + 254 * q^37 - 40 * q^38 - 114 * q^39 - 48 * q^40 + 42 * q^41 - 96 * q^42 - 52 * q^43 + 48 * q^44 + 54 * q^45 - 336 * q^46 - 96 * q^47 - 48 * q^48 - 87 * q^49 + 178 * q^50 + 378 * q^51 + 152 * q^52 + 198 * q^53 + 54 * q^54 + 72 * q^55 + 128 * q^56 - 60 * q^57 - 60 * q^58 - 660 * q^59 - 72 * q^60 - 538 * q^61 + 176 * q^62 - 144 * q^63 + 64 * q^64 + 228 * q^65 + 72 * q^66 + 884 * q^67 - 504 * q^68 - 504 * q^69 + 192 * q^70 + 792 * q^71 - 72 * q^72 + 218 * q^73 - 508 * q^74 + 267 * q^75 + 80 * q^76 - 192 * q^77 + 228 * q^78 - 520 * q^79 + 96 * q^80 + 81 * q^81 - 84 * q^82 - 492 * q^83 + 192 * q^84 - 756 * q^85 + 104 * q^86 - 90 * q^87 - 96 * q^88 + 810 * q^89 - 108 * q^90 - 608 * q^91 + 672 * q^92 + 264 * q^93 + 192 * q^94 + 120 * q^95 + 96 * q^96 + 1154 * q^97 + 174 * q^98 + 108 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\) 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	3
6.4.a.a	$6$	$4$	6.a	1.a	$1$	$1$	$1$	$0.354$	\(\Q\)	None	✓	✓	✓	✓	6.4.a.a	$1$	$0$	\(-2\)	\(-3\)	\(6\)	\(-16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)