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

• Label: 49.2.e
• Level: $49$
• Weight: $2$
• Character orbit: 49.e
• Rep. character: $\chi_{49}(8,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $9$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(9\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	30	30	0
Cusp forms	18	18	0
Eisenstein series	12	12	0

Trace form

18 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 9 * q^6 + 5 * q^8 - 14 * q^9 + 11 * q^10 - 6 * q^11 - 14 * q^12 + 7 * q^13 - 21 * q^14 - 3 * q^15 + 13 * q^16 + 4 * q^17 + 16 * q^18 - 22 * q^19 + 7 * q^20 + 21 * q^21 + 5 * q^22 - 12 * q^23 + 11 * q^24 + 14 * q^25 + 21 * q^26 + 12 * q^27 - 27 * q^29 + 40 * q^30 - 24 * q^31 - 3 * q^32 + 41 * q^33 - 37 * q^34 + 21 * q^35 + q^36 - 26 * q^37 + 25 * q^38 - 7 * q^39 - 15 * q^40 + 21 * q^41 - 49 * q^42 + 29 * q^43 - 13 * q^44 - 55 * q^45 + 3 * q^46 - 36 * q^47 + 12 * q^48 + 14 * q^49 - 76 * q^50 + 19 * q^51 - 7 * q^52 - 20 * q^53 + 50 * q^54 - 47 * q^55 - 14 * q^56 + 11 * q^57 - 31 * q^58 + 25 * q^59 - 35 * q^60 - 15 * q^61 + 61 * q^62 + 7 * q^63 + 27 * q^64 + 49 * q^65 - 31 * q^66 + 36 * q^67 + 28 * q^68 + 5 * q^69 + 35 * q^70 - 34 * q^71 + 4 * q^72 + 46 * q^73 + 59 * q^74 - 9 * q^75 + 56 * q^77 - 7 * q^78 + 44 * q^79 + 32 * q^80 - 48 * q^81 + 14 * q^82 - 21 * q^83 + 28 * q^84 + 11 * q^85 - 3 * q^86 + 43 * q^87 + 5 * q^88 - q^89 - 4 * q^90 - 91 * q^91 + 44 * q^92 - 65 * q^93 - 80 * q^94 - 8 * q^95 - 98 * q^96 - 28 * q^97 - 7 * q^98 - 20 * 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.e.a	$49$	$2$	49.e	49.e	$7$	$6$	$1$	$0.391$	\(\Q(\zeta_{14})\)	None		✓			49.2.e.a	$2$	$0$	\(-3\)	\(-3\)	\(6\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
49.2.e.b	$49$	$2$	49.e	49.e	$7$	$12$	$2$	$0.391$	\(\Q(\zeta_{21})\)	None		✓	✓		49.2.e.b	$2$	$0$	\(-2\)	\(0\)	\(-7\)	\(-7\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta_{11}-\beta_{9}+\cdots+\beta_{2})q^{2}+\cdots+(-\beta_{7}+\beta_{6}+\cdots+\beta_1)q^{3}+\cdots\)