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

• Label: 49.2.c
• Level: $49$
• Weight: $2$
• Character orbit: 49.c
• Rep. character: $\chi_{49}(18,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
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	18	10	8
Cusp forms	2	2	0
Eisenstein series	16	8	8

Trace form

2 * q - q^2 + q^4 - 6 * q^8 + 3 * q^9 - 4 * q^11 + q^16 + 3 * q^18 + 8 * q^22 - 8 * q^23 + 5 * q^25 + 4 * q^29 - 5 * q^32 + 6 * q^36 + 6 * q^37 - 24 * q^43 + 4 * q^44 - 8 * q^46 - 10 * q^50 + 10 * q^53 - 2 * q^58 + 14 * q^64 - 4 * q^67 + 32 * q^71 - 9 * q^72 + 6 * q^74 - 8 * q^79 - 9 * q^81 + 12 * q^86 + 12 * q^88 - 16 * q^92 - 24 * 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.c.a	$49$	$2$	49.c	7.c	$3$	$2$	$1$	$0.391$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)		✓	✓	✓	49.2.a.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)