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

• Label: 169.10.e
• Level: $169$
• Weight: $10$
• Character orbit: 169.e
• Rep. character: $\chi_{169}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $220$
• Sturm bound: $151$

Defining parameters

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(151\)

Dimensions

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

	Total	New	Old
Modular forms	288	240	48
Cusp forms	260	220	40
Eisenstein series	28	20	8

Trace form

220 * q + 3 * q^2 + 163 * q^3 + 26625 * q^4 + 3288 * q^6 - 1023 * q^7 - 643825 * q^9 - 38471 * q^10 + 94599 * q^11 + 543644 * q^12 - 594860 * q^14 - 754950 * q^15 - 6418507 * q^16 + 20282 * q^17 + 3879 * q^19 + 154815 * q^20 - 3525226 * q^22 - 2794297 * q^23 + 6472626 * q^24 - 71961670 * q^25 - 19165850 * q^27 - 4918980 * q^28 + 2623412 * q^29 - 24290202 * q^30 + 14390595 * q^32 + 34050309 * q^33 - 11422298 * q^35 + 136448447 * q^36 + 36102006 * q^37 + 73493292 * q^38 - 169892914 * q^40 - 30265110 * q^41 + 68864828 * q^42 - 45436289 * q^43 - 31870857 * q^45 - 121485864 * q^46 + 67999356 * q^48 + 473604501 * q^49 + 58518456 * q^50 - 58826550 * q^51 + 74493022 * q^53 + 393493974 * q^54 - 61919288 * q^55 - 845750 * q^56 - 470295633 * q^58 - 3987867 * q^59 + 382191770 * q^61 + 469180988 * q^62 - 506780166 * q^63 - 3271204598 * q^64 + 897463608 * q^66 + 944780397 * q^67 + 319542999 * q^68 - 604184623 * q^69 - 1318764849 * q^71 - 1409393649 * q^72 + 956559709 * q^74 + 931494703 * q^75 + 594798654 * q^76 + 1320745534 * q^77 - 1278780984 * q^79 + 968911845 * q^80 - 1529008034 * q^81 - 1961560907 * q^82 - 7275171300 * q^84 + 318942363 * q^85 + 1351115569 * q^87 + 3568916096 * q^88 + 2287100109 * q^89 + 7242770030 * q^90 - 9243079332 * q^92 + 1470324870 * q^93 + 3737820398 * q^94 - 5427836442 * q^95 - 7273214547 * q^97 + 1557570597 * q^98

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

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