Space of modular forms of level 169, weight 10, and Character 169.c

• Label: 169.10.c
• Level: $169$
• Weight: $10$
• Character orbit: 169.c
• Rep. character: $\chi_{169}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $222$
• Sturm bound: $151$

Defining parameters

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(151\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(169, [\chi])\).

	Total	New	Old
Modular forms	286	242	44
Cusp forms	258	222	36
Eisenstein series	28	20	8

Trace form

222 * q - 15 * q^2 - 161 * q^3 - 27391 * q^4 + 2280 * q^5 - 2118 * q^6 + 1939 * q^7 + 14478 * q^8 - 674934 * q^9 - 52647 * q^10 + 5433 * q^11 - 124704 * q^12 - 111404 * q^14 + 347428 * q^15 - 7413443 * q^16 - 219215 * q^17 + 38738 * q^18 + 311001 * q^19 - 927069 * q^20 - 1553030 * q^21 - 2845702 * q^22 - 923501 * q^23 + 4492800 * q^24 + 66481946 * q^25 + 10490350 * q^27 - 2697168 * q^28 - 11103157 * q^29 + 15865280 * q^30 + 23148076 * q^31 + 11868417 * q^32 - 14131427 * q^33 - 21859862 * q^34 - 24986012 * q^35 - 174280761 * q^36 + 29215749 * q^37 - 49044384 * q^38 - 62854462 * q^40 - 3328377 * q^41 - 31763512 * q^42 + 12740879 * q^43 - 31824624 * q^44 - 32857342 * q^45 - 36693338 * q^46 + 45575052 * q^47 + 56883882 * q^48 - 490925416 * q^49 + 49601730 * q^50 + 205622978 * q^51 + 67543252 * q^53 - 152965386 * q^54 + 22518790 * q^55 - 55125142 * q^56 - 523363230 * q^57 + 163479359 * q^58 + 32715855 * q^59 + 188638416 * q^60 + 334481719 * q^61 + 36179386 * q^62 - 166572574 * q^63 + 3852471562 * q^64 + 499833624 * q^66 - 112659045 * q^67 + 390188373 * q^68 - 23762119 * q^69 - 2040150992 * q^70 + 236450709 * q^71 - 995206683 * q^72 + 211881220 * q^73 + 870205585 * q^74 - 1291036075 * q^75 + 365789708 * q^76 + 2548672730 * q^77 + 1095441728 * q^79 - 580424625 * q^80 - 2775486643 * q^81 - 839892687 * q^82 - 2225691456 * q^83 + 1819004068 * q^84 - 1812284636 * q^85 - 291320076 * q^86 + 637427697 * q^87 - 4692711372 * q^88 + 1154379039 * q^89 + 9472918414 * q^90 + 5451271080 * q^92 - 3136878060 * q^93 - 1464667576 * q^94 - 977205840 * q^95 - 5906965568 * q^96 + 3616470111 * q^97 - 8263323501 * q^98 - 2262149268 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(169, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(169, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(169, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)