Space of modular forms of level 79, weight 2, and Character 79.g

• Label: 79.2.g
• Level: $79$
• Weight: $2$
• Character orbit: 79.g
• Rep. character: $\chi_{79}(2,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	79.g (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{39})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(13\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(79, [\chi])\).

	Total	New	Old
Modular forms	192	192	0
Cusp forms	144	144	0
Eisenstein series	48	48	0

Trace form

144 * q - 24 * q^2 - 26 * q^3 - 22 * q^4 - 25 * q^5 - 35 * q^6 - 26 * q^7 - 18 * q^9 - 6 * q^10 - 3 * q^11 - 16 * q^12 - 23 * q^13 + 35 * q^14 - 16 * q^15 - 18 * q^16 - 4 * q^17 + 7 * q^18 - 20 * q^19 - 50 * q^20 + 6 * q^21 + 16 * q^22 - 3 * q^23 + 57 * q^24 + 59 * q^25 - 37 * q^26 + 25 * q^27 - 19 * q^28 - 41 * q^29 - 13 * q^30 + 13 * q^31 + 36 * q^32 - 40 * q^33 + 34 * q^34 - 7 * q^35 - 25 * q^36 + 12 * q^37 + 12 * q^38 + 61 * q^39 - 3 * q^40 - 18 * q^41 + 43 * q^42 - 18 * q^43 + 63 * q^44 - 15 * q^45 + 92 * q^46 - 6 * q^47 - 16 * q^48 - 4 * q^49 + 68 * q^50 - 6 * q^51 - 22 * q^52 + 12 * q^53 + 74 * q^54 - 34 * q^55 + 138 * q^56 + 150 * q^57 - 66 * q^58 + 19 * q^59 + 292 * q^60 - 6 * q^61 - 64 * q^62 + 29 * q^63 - 34 * q^64 - 68 * q^65 + 40 * q^66 - 33 * q^67 - 127 * q^68 - 5 * q^69 - 54 * q^70 - 42 * q^71 - 226 * q^72 + 19 * q^73 - 59 * q^74 - 193 * q^75 - 122 * q^76 + 43 * q^77 - 130 * q^78 - 148 * q^79 - 22 * q^80 - 200 * q^81 - 109 * q^82 + 59 * q^83 - 133 * q^84 - 122 * q^85 - 3 * q^86 + 147 * q^87 - 236 * q^88 - 68 * q^89 - 4 * q^90 - 143 * q^91 - 64 * q^92 - 5 * q^93 + 38 * q^94 - 69 * q^95 + 184 * q^96 + 47 * q^97 + 11 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(79, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
79.2.g.a	$79$	$2$	79.g	79.g	$39$	$144$	$6$	$0.631$		None		✓	✓	✓	79.2.g.a	$2$	$0$	\(-24\)	\(-26\)	\(-25\)	\(-26\)		$\mathrm{SU}(2)[C_{39}]$