Space of modular forms of level 49, weight 6, and Character 49.e

• Label: 49.6.e
• Level: $49$
• Weight: $6$
• Character orbit: 49.e
• Rep. character: $\chi_{49}(8,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $138$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(49, [\chi])\).

	Total	New	Old
Modular forms	150	150	0
Cusp forms	138	138	0
Eisenstein series	12	12	0

Trace form

138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9 - 771 * q^10 + 410 * q^11 - 1316 * q^12 + 483 * q^13 + 2597 * q^14 + 2557 * q^15 - 7357 * q^16 - 1422 * q^17 - 2480 * q^18 - 6758 * q^19 - 3647 * q^20 - 399 * q^21 - 857 * q^22 - 2392 * q^23 - 3571 * q^24 - 8066 * q^25 - 343 * q^26 + 16396 * q^27 + 32102 * q^28 + 30341 * q^29 + 13716 * q^30 - 32712 * q^31 - 26993 * q^32 - 16775 * q^33 + 35163 * q^34 - 12019 * q^35 + 35461 * q^36 - 34872 * q^37 + 13383 * q^38 - 20671 * q^39 + 165169 * q^40 + 51233 * q^41 - 13741 * q^42 - 17203 * q^43 - 4267 * q^44 + 30777 * q^45 - 74611 * q^46 + 64264 * q^47 - 247084 * q^48 - 70350 * q^49 - 263036 * q^50 - 57453 * q^51 - 36043 * q^52 + 124590 * q^53 + 144840 * q^54 + 90977 * q^55 + 404404 * q^56 - 103899 * q^57 + 24861 * q^58 - 8079 * q^59 + 72065 * q^60 - 236659 * q^61 - 173227 * q^62 - 119805 * q^63 + 105381 * q^64 - 33383 * q^65 + 536577 * q^66 + 19716 * q^67 - 256340 * q^68 - 202795 * q^69 + 194803 * q^70 + 61778 * q^71 - 392108 * q^72 - 157760 * q^73 - 328319 * q^74 + 355167 * q^75 - 61334 * q^76 - 24402 * q^77 + 497217 * q^78 - 73876 * q^79 - 1340760 * q^80 - 815116 * q^81 + 248976 * q^82 + 303107 * q^83 + 1250354 * q^84 + 205487 * q^85 + 1083219 * q^86 + 197027 * q^87 + 1052915 * q^88 + 219783 * q^89 + 82170 * q^90 - 837235 * q^91 + 35936 * q^92 + 138365 * q^93 - 571908 * q^94 - 610016 * q^95 - 1054494 * q^96 + 762020 * q^97 - 2160767 * q^98 - 1090772 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.6.e.a	$49$	$6$	49.e	49.e	$7$	$138$	$23$	$7.859$		None		✓	✓	✓	49.6.e.a	$2$	$0$	\(-5\)	\(13\)	\(67\)	\(-56\)		$\mathrm{SU}(2)[C_{7}]$