Space of modular forms of level 7, weight 4, and trivial character

• Label: 7.4.a
• Level: $7$
• Weight: $4$
• Character orbit: 7.a
• Rep. character: $\chi_{7}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	7.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 \(M_{4}(\Gamma_0(7))\).

	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.

\(7\)	Dim
\(+\)	\(1\)

Trace form

q - q^2 - 2 * q^3 - 7 * q^4 + 16 * q^5 + 2 * q^6 - 7 * q^7 + 15 * q^8 - 23 * q^9 - 16 * q^10 - 8 * q^11 + 14 * q^12 + 28 * q^13 + 7 * q^14 - 32 * q^15 + 41 * q^16 + 54 * q^17 + 23 * q^18 - 110 * q^19 - 112 * q^20 + 14 * q^21 + 8 * q^22 + 48 * q^23 - 30 * q^24 + 131 * q^25 - 28 * q^26 + 100 * q^27 + 49 * q^28 - 110 * q^29 + 32 * q^30 + 12 * q^31 - 161 * q^32 + 16 * q^33 - 54 * q^34 - 112 * q^35 + 161 * q^36 - 246 * q^37 + 110 * q^38 - 56 * q^39 + 240 * q^40 + 182 * q^41 - 14 * q^42 + 128 * q^43 + 56 * q^44 - 368 * q^45 - 48 * q^46 + 324 * q^47 - 82 * q^48 + 49 * q^49 - 131 * q^50 - 108 * q^51 - 196 * q^52 - 162 * q^53 - 100 * q^54 - 128 * q^55 - 105 * q^56 + 220 * q^57 + 110 * q^58 + 810 * q^59 + 224 * q^60 - 488 * q^61 - 12 * q^62 + 161 * q^63 - 167 * q^64 + 448 * q^65 - 16 * q^66 + 244 * q^67 - 378 * q^68 - 96 * q^69 + 112 * q^70 - 768 * q^71 - 345 * q^72 - 702 * q^73 + 246 * q^74 - 262 * q^75 + 770 * q^76 + 56 * q^77 + 56 * q^78 + 440 * q^79 + 656 * q^80 + 421 * q^81 - 182 * q^82 - 1302 * q^83 - 98 * q^84 + 864 * q^85 - 128 * q^86 + 220 * q^87 - 120 * q^88 + 730 * q^89 + 368 * q^90 - 196 * q^91 - 336 * q^92 - 24 * q^93 - 324 * q^94 - 1760 * q^95 + 322 * q^96 + 294 * q^97 - 49 * q^98 + 184 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7
7.4.a.a	$7$	$4$	7.a	1.a	$1$	$1$	$1$	$0.413$	\(\Q\)	None	✓	✓	✓	✓	7.4.a.a	$1$	$0$	\(-1\)	\(-2\)	\(16\)	\(-7\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)