Space of modular forms of level 49, weight 2, and Character 49.g

• Label: 49.2.g
• Level: $49$
• Weight: $2$
• Character orbit: 49.g
• Rep. character: $\chi_{49}(2,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(49, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	48	48	0
Eisenstein series	24	24	0

Trace form

48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.2.g.a	$49$	$2$	49.g	49.g	$21$	$48$	$4$	$0.391$		None		✓	✓	✓	49.2.g.a	$2$	$0$	\(-13\)	\(-14\)	\(-14\)	\(-14\)		$\mathrm{SU}(2)[C_{21}]$