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

• Label: 197.14.e
• Level: $197$
• Weight: $14$
• Character orbit: 197.e
• Rep. character: $\chi_{197}(6,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1284$
• Sturm bound: $231$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	1296	1296	0
Cusp forms	1284	1284	0
Eisenstein series	12	12	0

Trace form

1284 * q - 7 * q^2 - 7 * q^3 + 835031 * q^4 - 7 * q^5 - 985870 * q^6 + 637661 * q^7 + 57337 * q^8 + 113728369 * q^9 + 13757961 * q^10 + 17362051 * q^11 - 57351 * q^12 - 7 * q^13 + 41668390 * q^15 - 4221686457 * q^16 - 7 * q^17 - 11160268 * q^18 - 921544204 * q^19 - 7 * q^21 + 2851547791 * q^22 - 1052318431 * q^23 - 2162444937 * q^24 + 52154544423 * q^25 - 9027790659 * q^26 + 7001459591 * q^27 + 9339198790 * q^28 + 4029350358 * q^29 + 9325687014 * q^30 - 19448615403 * q^31 + 1408884729 * q^32 - 54261242076 * q^33 - 35765685099 * q^34 - 7 * q^35 + 2880801180226 * q^36 + 109849835772 * q^37 - 57351 * q^38 + 100924790304 * q^39 + 2318682965 * q^40 + 61516331645 * q^41 - 118839135084 * q^42 + 121762984926 * q^43 + 359775694117 * q^44 + 249927658757 * q^45 + 67702289599 * q^46 + 292998509612 * q^47 + 273745919993 * q^48 - 2124778939883 * q^49 - 1372261194451 * q^50 + 215705550459 * q^51 - 1237574873906 * q^52 - 122512727593 * q^53 - 353926412356 * q^54 + 1220422235965 * q^55 + 1708563003938 * q^56 + 1120732826038 * q^57 + 400271979513 * q^58 - 1567475845 * q^59 + 270862037463 * q^60 + 1019634203987 * q^61 + 3503251228317 * q^62 - 4189069175894 * q^63 + 12455572228523 * q^64 - 2209778962144 * q^65 + 1333786063778 * q^66 - 6515229693777 * q^67 - 2242060731310 * q^70 - 3518902454760 * q^71 + 5643464923824 * q^72 - 1667595396761 * q^73 + 1448925519993 * q^74 + 6114276222642 * q^75 - 8691849527818 * q^76 + 11094832710647 * q^78 - 20549979749131 * q^79 + 469762041 * q^80 - 49476775727501 * q^81 - 7 * q^82 + 16155369605122 * q^83 - 13558134450789 * q^85 + 7949009052460 * q^86 + 38672456829290 * q^88 + 13437250770867 * q^89 + 130525951112045 * q^90 + 11300980303781 * q^91 + 45675024597397 * q^92 - 4948656954964 * q^93 - 85960476064477 * q^94 + 65009579021107 * q^95 + 40869436917830 * q^96 - 20267871468757 * q^97 - 39105912674486 * q^98 + 44744920030657 * 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.