Space of modular forms of level 5, weight 4, and trivial character

• Label: 5.4.a
• Level: $5$
• Weight: $4$
• Character orbit: 5.a
• Rep. character: $\chi_{5}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(5))\).

	Total	New	Old
Modular forms	3	1	2
Cusp forms	1	1	0
Eisenstein series	2	0	2

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

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

Trace form

q - 4 * q^2 + 2 * q^3 + 8 * q^4 - 5 * q^5 - 8 * q^6 + 6 * q^7 - 23 * q^9 + 20 * q^10 + 32 * q^11 + 16 * q^12 - 38 * q^13 - 24 * q^14 - 10 * q^15 - 64 * q^16 + 26 * q^17 + 92 * q^18 + 100 * q^19 - 40 * q^20 + 12 * q^21 - 128 * q^22 - 78 * q^23 + 25 * q^25 + 152 * q^26 - 100 * q^27 + 48 * q^28 - 50 * q^29 + 40 * q^30 - 108 * q^31 + 256 * q^32 + 64 * q^33 - 104 * q^34 - 30 * q^35 - 184 * q^36 + 266 * q^37 - 400 * q^38 - 76 * q^39 + 22 * q^41 - 48 * q^42 + 442 * q^43 + 256 * q^44 + 115 * q^45 + 312 * q^46 - 514 * q^47 - 128 * q^48 - 307 * q^49 - 100 * q^50 + 52 * q^51 - 304 * q^52 + 2 * q^53 + 400 * q^54 - 160 * q^55 + 200 * q^57 + 200 * q^58 + 500 * q^59 - 80 * q^60 - 518 * q^61 + 432 * q^62 - 138 * q^63 - 512 * q^64 + 190 * q^65 - 256 * q^66 + 126 * q^67 + 208 * q^68 - 156 * q^69 + 120 * q^70 + 412 * q^71 - 878 * q^73 - 1064 * q^74 + 50 * q^75 + 800 * q^76 + 192 * q^77 + 304 * q^78 + 600 * q^79 + 320 * q^80 + 421 * q^81 - 88 * q^82 + 282 * q^83 + 96 * q^84 - 130 * q^85 - 1768 * q^86 - 100 * q^87 - 150 * q^89 - 460 * q^90 - 228 * q^91 - 624 * q^92 - 216 * q^93 + 2056 * q^94 - 500 * q^95 + 512 * q^96 + 386 * q^97 + 1228 * q^98 - 736 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
5.4.a.a	$5$	$4$	5.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	✓	✓	✓	5.4.a.a	$1$	$0$	\(-4\)	\(2\)	\(-5\)	\(6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)