Space of modular forms of level 49, weight 22, and Character 49.c

• Label: 49.22.c
• Level: $49$
• Weight: $22$
• Character orbit: 49.c
• Rep. character: $\chi_{49}(18,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $136$
• Sturm bound: $102$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(102\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(49, [\chi])\).

	Total	New	Old
Modular forms	204	144	60
Cusp forms	188	136	52
Eisenstein series	16	8	8

Trace form

136 * q - 573 * q^2 - 118097 * q^3 - 70810345 * q^4 - 19296893 * q^5 + 457302020 * q^6 + 1280412774 * q^8 - 218667013405 * q^9 - 45908292458 * q^10 + 116094841045 * q^11 - 703726516612 * q^12 - 573150555348 * q^13 + 2880852458002 * q^15 - 62888578987685 * q^16 - 3631296873225 * q^17 + 32035715280937 * q^18 - 56849486179647 * q^19 + 211235752093016 * q^20 + 696271124695836 * q^22 + 159906108938871 * q^23 + 151975129265904 * q^24 - 5811119052144029 * q^25 + 1358522589413276 * q^26 + 2144448281577238 * q^27 - 15989169328136488 * q^29 + 5944484277239358 * q^30 - 2915918111714909 * q^31 - 8497750454589467 * q^32 - 14438281026776999 * q^33 + 79038877574366724 * q^34 + 289226695395829850 * q^36 + 70239327775907151 * q^37 - 69816975237291142 * q^38 - 223105560390102670 * q^39 - 327938659319189184 * q^40 + 485968527188727716 * q^41 - 120786450050234984 * q^43 + 819504456563159268 * q^44 + 37395922860484930 * q^45 - 1455493298272396210 * q^46 - 545845114015708227 * q^47 + 4323454314028504928 * q^48 - 1463760786075534878 * q^50 - 1168590189847114457 * q^51 + 2470837410767658632 * q^52 + 3073284490028750019 * q^53 - 355603765001582734 * q^54 + 4587818432221886582 * q^55 - 7741323642927907794 * q^57 - 332930357316357442 * q^58 - 7474478541444602961 * q^59 + 29178095550829202852 * q^60 + 2848450223489054583 * q^61 - 63246313374361735548 * q^62 + 158367521183028357338 * q^64 - 27003943934162856402 * q^65 + 34922560371104300090 * q^66 - 45821203126569899419 * q^67 + 60830600544042602196 * q^68 - 55070614676968282518 * q^69 + 21849754602160092880 * q^71 - 56754182965666706259 * q^72 + 22389609053337927163 * q^73 + 295470313135892390396 * q^74 - 84570010377850408348 * q^75 - 71802870184863662824 * q^76 + 338865402408674009064 * q^78 + 217718684540539025495 * q^79 - 226029126485786363824 * q^80 - 1150569709194316278040 * q^81 - 126519604886693145484 * q^82 + 1235016850633512172968 * q^83 - 433811807898865883990 * q^85 - 97860353488040513984 * q^86 - 367683551076552943442 * q^87 - 2242483408387636647912 * q^88 - 31327966399121384405 * q^89 + 1322424440541914944136 * q^90 - 5430844411737840523608 * q^92 + 998275554458240910079 * q^93 - 279079228503504697758 * q^94 - 578851801795517216711 * q^95 - 81057395943474767264 * q^96 - 234002595919330799036 * q^97 + 6758782982330798119028 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{22}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(49, [\chi]) \simeq \) \(S_{22}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)