Space of modular forms of level 338, weight 10, and Character 338.c

• Label: 338.10.c
• Level: $338$
• Weight: $10$
• Character orbit: 338.c
• Rep. character: $\chi_{338}(191,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $230$
• Sturm bound: $455$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(455\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(338, [\chi])\).

	Total	New	Old
Modular forms	846	230	616
Cusp forms	790	230	560
Eisenstein series	56	0	56

Trace form

230 * q + 16 * q^2 + 162 * q^3 - 29440 * q^4 - 1558 * q^5 - 2850 * q^7 - 8192 * q^8 - 743089 * q^9 + 41712 * q^10 - 39326 * q^11 - 82944 * q^12 - 192 * q^14 - 360776 * q^15 - 7536640 * q^16 - 29677 * q^17 - 1792928 * q^18 + 354718 * q^19 + 199424 * q^20 - 2116244 * q^21 + 1686624 * q^22 - 285018 * q^23 + 96570928 * q^25 - 2132544 * q^27 - 729600 * q^28 + 13479275 * q^29 - 8752288 * q^30 - 26782816 * q^31 + 1048576 * q^32 + 25872262 * q^33 + 11098016 * q^34 + 29079774 * q^35 - 190230784 * q^36 - 21602195 * q^37 - 533056 * q^38 - 21356544 * q^40 + 274845 * q^41 + 77984864 * q^42 + 96553162 * q^43 + 20134912 * q^44 - 32348653 * q^45 - 37451840 * q^46 - 174846344 * q^47 + 10616832 * q^48 - 613624627 * q^49 + 46924736 * q^50 - 148180088 * q^51 + 121809030 * q^53 - 55501056 * q^54 - 369925248 * q^55 + 24576 * q^56 + 434760508 * q^57 + 122216176 * q^58 - 18272290 * q^59 + 184717312 * q^60 - 410056717 * q^61 + 68760768 * q^62 - 116485392 * q^63 + 3858759680 * q^64 - 984856832 * q^66 + 320197838 * q^67 - 7597312 * q^68 + 265875206 * q^69 + 568530048 * q^70 - 238656386 * q^71 + 229494784 * q^72 - 781839782 * q^73 - 412530256 * q^74 + 1252916112 * q^75 + 90807808 * q^76 - 2258638332 * q^77 - 226843360 * q^79 + 51052544 * q^80 - 5362132075 * q^81 - 131101264 * q^82 + 3041665536 * q^83 + 270879232 * q^84 + 2913176369 * q^85 - 692734208 * q^86 - 2287063886 * q^87 + 431775744 * q^88 - 1257526860 * q^89 - 1220362272 * q^90 + 145929216 * q^92 + 3106387752 * q^93 + 397776864 * q^94 - 1424692620 * q^95 - 3307136932 * q^97 + 3635475600 * q^98 + 3704648192 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(338, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)