Space of modular forms of level 338, weight 6, and Character 338.e

• Label: 338.6.e
• Level: $338$
• Weight: $6$
• Character orbit: 338.e
• Rep. character: $\chi_{338}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $128$
• Sturm bound: $273$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(273\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(338, [\chi])\).

	Total	New	Old
Modular forms	484	128	356
Cusp forms	428	128	300
Eisenstein series	56	0	56

Trace form

128 * q + 1024 * q^4 - 360 * q^7 - 4964 * q^9 + 368 * q^10 - 504 * q^11 + 2096 * q^14 - 2112 * q^15 - 16384 * q^16 + 2452 * q^17 + 6888 * q^19 - 1440 * q^20 - 3352 * q^22 - 7764 * q^23 - 82580 * q^25 - 2316 * q^27 - 5760 * q^28 - 12020 * q^29 + 13400 * q^30 + 18780 * q^33 - 30494 * q^35 + 79424 * q^36 + 882 * q^37 - 26320 * q^38 + 11776 * q^40 - 44346 * q^41 - 36872 * q^42 + 50076 * q^43 + 158850 * q^45 + 33408 * q^46 + 141410 * q^49 - 11040 * q^50 - 144772 * q^51 + 193368 * q^53 - 1296 * q^54 - 21272 * q^55 + 16768 * q^56 + 73488 * q^58 - 74832 * q^59 - 53836 * q^61 + 5952 * q^62 - 156528 * q^63 - 524288 * q^64 - 63616 * q^66 - 85104 * q^67 - 39232 * q^68 + 107268 * q^69 + 106320 * q^71 + 78336 * q^72 - 105968 * q^74 - 278142 * q^75 + 110208 * q^76 + 298368 * q^77 + 23456 * q^79 - 23040 * q^80 - 408344 * q^81 + 74864 * q^82 - 53952 * q^84 + 148986 * q^85 + 74708 * q^87 + 53632 * q^88 - 93108 * q^89 - 370224 * q^90 - 248448 * q^92 - 107616 * q^93 - 133832 * q^94 - 172184 * q^95 - 147156 * q^97 - 46752 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(338, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)