Space of modular forms of level 338, weight 8, and Character 338.k

• Label: 338.8.k
• Level: $338$
• Weight: $8$
• Character orbit: 338.k
• Rep. character: $\chi_{338}(17,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $2544$
• Sturm bound: $364$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	338.k (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{78})\)
Sturm bound:			\(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(338, [\chi])\).

	Total	New	Old
Modular forms	7680	2544	5136
Cusp forms	7584	2544	5040
Eisenstein series	96	0	96

Trace form

2544 * q - 6784 * q^4 - 2520 * q^7 + 76126 * q^9 - 2432 * q^10 + 8496 * q^11 + 217964 * q^13 - 30944 * q^14 - 5420 * q^15 + 434176 * q^16 - 31186 * q^17 + 54432 * q^19 + 16128 * q^20 - 255552 * q^22 - 28868 * q^23 + 3266628 * q^25 - 51072 * q^26 - 185316 * q^27 - 161280 * q^28 + 305454 * q^29 + 2937136 * q^30 - 475436 * q^31 - 486300 * q^33 - 25234 * q^35 - 4872064 * q^36 + 68280 * q^37 + 1413728 * q^38 + 6152068 * q^39 + 48128 * q^40 + 1288008 * q^41 - 439952 * q^42 - 525628 * q^43 + 4551890 * q^45 + 188928 * q^46 + 6709898 * q^47 - 7118202 * q^49 - 85248 * q^50 + 15488670 * q^51 - 354560 * q^52 - 5689628 * q^53 - 14412000 * q^54 - 9536552 * q^55 - 990208 * q^56 - 17748354 * q^57 + 5386336 * q^58 - 1799280 * q^59 - 11411712 * q^60 + 2151042 * q^61 + 420416 * q^62 + 35767670 * q^63 + 55574528 * q^64 + 11518020 * q^65 - 10951808 * q^66 + 29937116 * q^67 + 1995904 * q^68 - 15646868 * q^69 + 25212444 * q^71 - 4423680 * q^72 - 33286960 * q^74 + 160546962 * q^75 - 5413760 * q^76 + 24127280 * q^77 + 22023040 * q^78 - 41910400 * q^79 + 1032192 * q^80 + 59653762 * q^81 - 12229152 * q^82 - 110513780 * q^83 - 17311488 * q^84 - 25239926 * q^85 - 39120432 * q^86 - 9575976 * q^87 - 1362944 * q^88 - 10609452 * q^89 - 2150048 * q^90 + 64273204 * q^91 - 3695104 * q^92 - 116234902 * q^93 - 58060432 * q^94 - 128610376 * q^95 - 95073006 * q^97 - 19031040 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(338, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)