Space of modular forms of level 49, weight 10, and Character 49.e

• Label: 49.10.e
• Level: $49$
• Weight: $10$
• Character orbit: 49.e
• Rep. character: $\chi_{49}(8,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $246$
• Newform subspaces: $1$
• Sturm bound: $46$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(46\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(49, [\chi])\).

	Total	New	Old
Modular forms	258	258	0
Cusp forms	246	246	0
Eisenstein series	12	12	0

Trace form

246 * q - 5 * q^2 - 5 * q^3 - 10245 * q^4 + 677 * q^5 + 14971 * q^6 - 2408 * q^7 + 305 * q^8 - 340374 * q^9 + 54469 * q^10 - 75759 * q^11 - 139412 * q^12 + 46305 * q^13 + 1170141 * q^14 + 256627 * q^15 - 3026557 * q^16 + 503827 * q^17 + 637072 * q^18 - 2946428 * q^19 + 3484033 * q^20 - 408177 * q^21 + 7202367 * q^22 + 2413413 * q^23 + 11943437 * q^24 - 17020366 * q^25 + 15589497 * q^26 + 4712839 * q^27 + 2972214 * q^28 - 11313279 * q^29 - 21765324 * q^30 - 44124596 * q^31 - 12214833 * q^32 + 35900569 * q^33 + 65839723 * q^34 + 27636651 * q^35 - 100148507 * q^36 + 22907425 * q^37 - 16372025 * q^38 - 56169799 * q^39 - 114764911 * q^40 + 11190963 * q^41 + 114708755 * q^42 + 56287695 * q^43 + 186916085 * q^44 + 195096717 * q^45 - 103419515 * q^46 + 160667589 * q^47 + 234961172 * q^48 - 158295564 * q^49 - 623579836 * q^50 + 11516253 * q^51 - 175372043 * q^52 - 210504845 * q^53 + 377945472 * q^54 - 273362703 * q^55 - 966623084 * q^56 + 419182848 * q^57 + 158850157 * q^58 + 156767389 * q^59 + 1407468545 * q^60 + 363730323 * q^61 + 402403405 * q^62 - 31489962 * q^63 + 224735525 * q^64 + 229206397 * q^65 - 230460543 * q^66 + 535226512 * q^67 - 2705167220 * q^68 - 956377291 * q^69 - 2375401917 * q^70 + 737795921 * q^71 + 1306721476 * q^72 + 165534623 * q^73 + 342045113 * q^74 + 1357064817 * q^75 + 2152951626 * q^76 + 753031517 * q^77 + 621122145 * q^78 + 800430444 * q^79 - 4527272440 * q^80 - 1267980958 * q^81 - 1433640656 * q^82 + 1723072407 * q^83 - 5668681774 * q^84 + 1216605257 * q^85 - 2241100389 * q^86 - 2895860425 * q^87 - 2875486333 * q^88 + 3039923339 * q^89 + 11763673050 * q^90 + 1021016535 * q^91 + 752583488 * q^92 - 1495708144 * q^93 + 6470422772 * q^94 - 1239109886 * q^95 + 10709780130 * q^96 - 8880348372 * q^97 - 7858722655 * q^98 - 9994213472 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.10.e.a	$49$	$10$	49.e	49.e	$7$	$246$	$41$	$25.237$		None		✓	✓	✓	49.10.e.a	$2$	$0$	\(-5\)	\(-5\)	\(677\)	\(-2408\)		$\mathrm{SU}(2)[C_{7}]$