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

• Label: 197.14.h
• Level: $197$
• Weight: $14$
• Character orbit: 197.h
• Rep. character: $\chi_{197}(4,\cdot)$
• Character field: $\Q(\zeta_{98})$
• Dimension: $8988$
• Sturm bound: $231$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.h (of order \(98\) and degree \(42\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{98})\)
Sturm bound:			\(231\)

Dimensions

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

	Total	New	Old
Modular forms	9072	9072	0
Cusp forms	8988	8988	0
Eisenstein series	84	84	0

Trace form

8988 * q - 42 * q^2 - 42 * q^3 + 58576 * q^4 - 42 * q^5 + 653149 * q^6 - 570416 * q^7 - 57386 * q^8 - 42 * q^9 - 17281292 * q^10 - 17362100 * q^11 + 57302 * q^12 - 42 * q^13 - 238473690 * q^15 + 616875112 * q^16 - 42 * q^17 + 11160219 * q^18 + 1317284633 * q^19 - 49 * q^20 - 42 * q^21 - 2087933694 * q^22 - 42 * q^23 + 7782670294 * q^24 - 42 * q^25 + 12266811606 * q^26 - 7001459640 * q^27 - 15469506451 * q^28 - 95854458371 * q^29 - 9325687063 * q^30 + 19448615354 * q^31 - 1408884778 * q^32 + 78255251599 * q^33 + 27256178390 * q^34 - 42 * q^35 - 3434193533407 * q^36 - 120201345803 * q^37 + 57302 * q^38 - 10674616743 * q^39 + 44860190746 * q^40 - 38525717468 * q^41 + 284075937012 * q^42 - 197072963836 * q^43 + 2158654164702 * q^44 - 249927658806 * q^45 - 67702289648 * q^46 - 209875554287 * q^47 - 273745920042 * q^48 - 1061161041066 * q^49 + 1372261194402 * q^50 - 525862742566 * q^51 + 1237574873857 * q^52 - 42 * q^53 + 1514659462617 * q^54 - 1451283773604 * q^55 - 1705274669651 * q^56 - 10965551967041 * q^57 - 10227970749738 * q^58 - 1486154291146 * q^59 + 3369053518614 * q^60 - 698602605134 * q^61 - 809372710468 * q^62 + 1952032412239 * q^63 + 6068712741406 * q^64 + 5322360361549 * q^65 - 1333786063827 * q^66 + 6515229693728 * q^67 - 49 * q^68 - 49 * q^69 + 51269531208 * q^70 - 15275293227173 * q^71 + 34500763951136 * q^72 + 1667595396712 * q^73 - 1448925520042 * q^74 - 6114276222691 * q^75 + 3069061645153 * q^76 - 49 * q^77 - 11094832710696 * q^78 + 20549979749082 * q^79 - 469762090 * q^80 - 6382833710414 * q^81 - 42 * q^82 - 10034280083331 * q^83 + 639974006735 * q^84 - 53752953460598 * q^85 + 69781580600739 * q^86 - 49 * q^87 - 55949994187381 * q^88 - 13437250770916 * q^89 - 102774639072840 * q^90 - 11300980303830 * q^91 - 5378885148714 * q^92 + 18115725136537 * q^93 + 85960476064428 * q^94 - 65009579021156 * q^95 - 92926104562445 * q^96 + 3151454559750 * q^97 + 43853474184380 * q^98 - 54472232989461 * 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.