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

• Label: 338.8.e
• Level: $338$
• Weight: $8$
• Character orbit: 338.e
• Rep. character: $\chi_{338}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $180$
• Sturm bound: $364$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(364\)

Dimensions

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

	Total	New	Old
Modular forms	664	180	484
Cusp forms	608	180	428
Eisenstein series	56	0	56

Trace form

180 * q + 5760 * q^4 - 2520 * q^7 - 66758 * q^9 - 2432 * q^10 + 8496 * q^11 - 38176 * q^14 - 51648 * q^15 - 368640 * q^16 - 51854 * q^17 + 54432 * q^19 + 16128 * q^20 + 13264 * q^22 + 43988 * q^23 - 2718708 * q^25 - 82524 * q^27 - 161280 * q^28 + 386658 * q^29 - 320944 * q^30 - 486300 * q^33 + 591730 * q^35 + 4272512 * q^36 + 68280 * q^37 + 705952 * q^38 - 311296 * q^40 + 1288008 * q^41 - 376688 * q^42 - 45092 * q^43 - 5743980 * q^45 + 188928 * q^46 + 14764200 * q^49 - 85248 * q^50 - 2615860 * q^51 - 1581276 * q^53 + 4074624 * q^54 + 2140472 * q^55 - 1221632 * q^56 - 3504000 * q^58 - 1799280 * q^59 + 7100958 * q^61 + 5120704 * q^62 + 8609760 * q^63 - 47185920 * q^64 - 4930432 * q^66 + 7094400 * q^67 + 3318656 * q^68 - 20407764 * q^69 - 25958520 * q^71 - 4423680 * q^72 + 3900224 * q^74 + 21214050 * q^75 + 3483648 * q^76 + 17027680 * q^77 - 26376576 * q^79 + 1032192 * q^80 - 28162034 * q^81 - 12175328 * q^82 - 17311488 * q^84 - 7123932 * q^85 + 22537580 * q^87 - 848896 * q^88 - 10609452 * q^89 - 5991264 * q^90 + 5630464 * q^92 + 52747080 * q^93 + 19941680 * q^94 - 45531720 * q^95 - 83706300 * 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

\( S_{8}^{\mathrm{old}}(338, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)