Space of modular forms of level 343, weight 2, and Character 343.e

• Label: 343.2.e
• Level: $343$
• Weight: $2$
• Character orbit: 343.e
• Rep. character: $\chi_{343}(50,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $114$
• Newform subspaces: $4$
• Sturm bound: $65$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(65\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(343, [\chi])\).

	Total	New	Old
Modular forms	234	174	60
Cusp forms	150	114	36
Eisenstein series	84	60	24

Trace form

114 * q + 5 * q^2 + 3 * q^3 - 11 * q^4 + q^5 + 9 * q^6 - 35 * q^8 + 4 * q^9 - 11 * q^10 + 6 * q^11 + 14 * q^12 - 7 * q^13 - 27 * q^15 - 17 * q^16 - 4 * q^17 + 8 * q^18 + 22 * q^19 - 7 * q^20 - 35 * q^22 + 12 * q^23 - 11 * q^24 - 12 * q^25 - 21 * q^26 - 12 * q^27 - 3 * q^29 - 4 * q^30 + 24 * q^31 + 27 * q^32 - 41 * q^33 + 37 * q^34 - 23 * q^36 - 44 * q^37 - 25 * q^38 - 63 * q^39 + 15 * q^40 - 21 * q^41 - 31 * q^43 + 61 * q^44 + 55 * q^45 + 21 * q^46 + 36 * q^47 - 12 * q^48 + 4 * q^50 + 17 * q^51 + 7 * q^52 + 20 * q^53 - 50 * q^54 + 47 * q^55 - 13 * q^57 + 31 * q^58 - 25 * q^59 + 35 * q^60 + 15 * q^61 - 61 * q^62 - 37 * q^64 - 49 * q^65 + 31 * q^66 - 8 * q^67 - 28 * q^68 - 5 * q^69 + 4 * q^71 - 88 * q^72 - 46 * q^73 - 35 * q^74 + 9 * q^75 + 49 * q^78 - 16 * q^79 - 32 * q^80 + 74 * q^81 - 14 * q^82 + 21 * q^83 - 41 * q^85 + 45 * q^86 - 43 * q^87 + 61 * q^88 + q^89 + 4 * q^90 - 32 * q^92 + 3 * q^93 + 80 * q^94 - 142 * q^95 + 98 * q^96 + 28 * q^97 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(343, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
343.2.e.a	$343$	$2$	343.e	49.e	$7$	$6$	$1$	$2.739$	\(\Q(\zeta_{14})\)	None					49.2.e.a	$2$	$0$	\(-3\)	\(3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
343.2.e.b	$343$	$2$	343.e	49.e	$7$	$12$	$2$	$2.739$	\(\Q(\zeta_{21})\)	None					49.2.e.b	$2$	$0$	\(-2\)	\(0\)	\(7\)	\(0\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta_{11}-\beta_{9}+\beta_{5})q^{2}+(\beta_{7}-\beta_{6}+\beta_{2}-\beta_1)q^{3}+\cdots\)
343.2.e.c	$343$	$2$	343.e	49.e	$7$	$48$	$8$	$2.739$		None					49.2.g.a	$2$	$0$	\(5\)	\(-7\)	\(-7\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$
343.2.e.d	$343$	$2$	343.e	49.e	$7$	$48$	$8$	$2.739$		None					49.2.g.a	$2$	$0$	\(5\)	\(7\)	\(7\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(343, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(343, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)