Space of modular forms of level 197, weight 10, and Character 197.d

• Label: 197.10.d
• Level: $197$
• Weight: $10$
• Character orbit: 197.d
• Rep. character: $\chi_{197}(36,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $882$
• Sturm bound: $165$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(165\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(197, [\chi])\).

	Total	New	Old
Modular forms	894	894	0
Cusp forms	882	882	0
Eisenstein series	12	12	0

Trace form

882 * q - 23 * q^2 - 5 * q^3 - 35245 * q^4 - 2849 * q^5 - 10574 * q^6 + 32999 * q^7 + 49347 * q^8 - 938228 * q^9 + 96557 * q^10 + 221837 * q^11 + 77305 * q^12 - 46317 * q^13 - 974584 * q^14 + 398455 * q^15 - 10064593 * q^16 - 715877 * q^17 - 481278 * q^18 - 2545664 * q^19 - 715492 * q^20 + 1333537 * q^21 + 4772547 * q^22 - 3562223 * q^23 + 8043679 * q^24 - 54489170 * q^25 - 2825363 * q^26 - 2896697 * q^27 + 5627030 * q^28 + 15314421 * q^29 + 9409888 * q^30 - 22800941 * q^31 + 32657425 * q^32 - 96294774 * q^33 - 941515 * q^34 + 9474021 * q^35 + 1187444610 * q^36 - 47625095 * q^37 - 53850731 * q^38 + 43537791 * q^39 + 125164449 * q^40 + 66525545 * q^41 - 83920770 * q^42 - 72880371 * q^43 + 203277289 * q^44 + 204931589 * q^45 - 102743355 * q^46 - 111574393 * q^47 - 97193867 * q^48 - 851526162 * q^49 + 432266873 * q^50 - 53220027 * q^51 - 127650572 * q^52 + 46332353 * q^53 + 40204070 * q^54 + 493254125 * q^55 + 293501272 * q^56 + 180389846 * q^57 - 627505665 * q^58 + 24665545 * q^59 - 944238971 * q^60 + 806405437 * q^61 + 265408787 * q^62 + 315393321 * q^63 - 2850881269 * q^64 - 1342451173 * q^65 + 708955728 * q^66 + 705245181 * q^67 - 3169417952 * q^68 + 316638254 * q^69 - 749508688 * q^70 + 2262879809 * q^71 - 868725360 * q^72 - 154098121 * q^73 + 498916005 * q^74 + 939115461 * q^75 - 873307600 * q^76 + 1890823474 * q^77 - 1293709829 * q^78 + 1396689245 * q^79 - 409070455 * q^80 - 6790539154 * q^81 + 1620121953 * q^82 - 3379751740 * q^83 - 493015176 * q^84 + 1268795481 * q^85 + 1694842400 * q^86 + 376250498 * q^87 + 728632396 * q^88 - 3056262199 * q^89 + 8970607881 * q^90 - 3649363745 * q^91 + 3142709653 * q^92 - 800212434 * q^93 + 7316677515 * q^94 - 8287517336 * q^95 + 5047374768 * q^96 + 2498465755 * q^97 + 2936361348 * q^98 + 7760889278 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

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