Space of modular forms of level 197, weight 14, and Character 197.d

• Label: 197.14.d
• Level: $197$
• Weight: $14$
• Character orbit: 197.d
• Rep. character: $\chi_{197}(36,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $1278$
• Sturm bound: $231$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(231\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(197, [\chi])\).

	Total	New	Old
Modular forms	1290	1290	0
Cusp forms	1278	1278	0
Eisenstein series	12	12	0

Trace form

1278 * q - 71 * q^2 - 5 * q^3 - 822029 * q^4 + 10501 * q^5 - 953102 * q^6 - 167075 * q^7 + 347779 * q^8 - 111071174 * q^9 - 24028563 * q^10 + 6851553 * q^11 + 4874233 * q^12 + 35067405 * q^13 + 87236072 * q^14 + 49456600 * q^15 - 3331550161 * q^16 - 118781471 * q^17 + 37850658 * q^18 - 961317956 * q^19 + 84061468 * q^20 + 292293133 * q^21 - 1006128605 * q^22 + 1712247721 * q^23 + 1491356287 * q^24 - 53938480130 * q^25 - 2420345091 * q^26 + 333256255 * q^27 + 13194239302 * q^28 + 19338993317 * q^29 + 16889183248 * q^30 + 15747651105 * q^31 + 19502649777 * q^32 + 28676656176 * q^33 + 28806370837 * q^34 + 961430221 * q^35 + 2441851897026 * q^36 + 39485485587 * q^37 - 33184650123 * q^38 - 16127903370 * q^39 - 257157552191 * q^40 - 4750659865 * q^41 + 181322886510 * q^42 + 128559595000 * q^43 - 226271516759 * q^44 - 709830350506 * q^45 + 531978852965 * q^46 + 110284743908 * q^47 + 525581620789 * q^48 - 2902524598086 * q^49 + 1207969253513 * q^50 - 263188481133 * q^51 - 1002648836732 * q^52 - 504468579587 * q^53 + 250567161206 * q^54 - 952607870395 * q^55 - 728194980136 * q^56 - 567765697720 * q^57 - 1057572312193 * q^58 - 2039065000737 * q^59 - 1064343710651 * q^60 - 252823813767 * q^61 + 1067351811123 * q^62 - 3947225614680 * q^63 - 12716394134645 * q^64 + 1107649848367 * q^65 + 1603345995408 * q^66 + 5790561699739 * q^67 + 3868059928096 * q^68 + 275170410614 * q^69 + 2796356360512 * q^70 + 6071021994338 * q^71 + 2900414862000 * q^72 - 443749808477 * q^73 - 4629472851019 * q^74 + 1598649351516 * q^75 + 8039525286400 * q^76 - 13249185042682 * q^77 + 2966095571179 * q^78 - 19160522060233 * q^79 + 1564042413705 * q^80 - 47833191244864 * q^81 - 5833702556031 * q^82 - 51604336063378 * q^83 - 3200533840200 * q^84 + 44817824206731 * q^85 - 17699276541616 * q^86 - 11707978292014 * q^87 - 13027939009620 * q^88 + 6794059806437 * q^89 + 105905302340601 * q^90 + 32558811541969 * q^91 + 91770983907733 * q^92 - 3088726750308 * q^93 + 75964532381547 * q^94 + 28681340790059 * q^95 + 44550276955872 * q^96 - 1316849765195 * q^97 - 24479051669388 * q^98 + 44106215633177 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

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