Space of modular forms of level 245, weight 6, and Character 245.e

• Label: 245.6.e
• Level: $245$
• Weight: $6$
• Character orbit: 245.e
• Rep. character: $\chi_{245}(116,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $132$
• Sturm bound: $168$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(245, [\chi])\).

	Total	New	Old
Modular forms	296	132	164
Cusp forms	264	132	132
Eisenstein series	32	0	32

Trace form

132 * q - 4 * q^2 + 18 * q^3 - 1068 * q^4 + 50 * q^5 - 80 * q^6 - 456 * q^8 - 4774 * q^9 + 200 * q^10 - 1598 * q^11 - 514 * q^12 - 3688 * q^13 + 2200 * q^15 - 12208 * q^16 + 3396 * q^17 + 1398 * q^18 - 1736 * q^19 - 8600 * q^20 + 13336 * q^22 + 1738 * q^23 - 9208 * q^24 - 41250 * q^25 - 4822 * q^26 - 19716 * q^27 - 33096 * q^29 - 3800 * q^30 - 2012 * q^31 + 32912 * q^32 + 1588 * q^33 + 77032 * q^34 + 181952 * q^36 - 52260 * q^37 - 27648 * q^38 - 30070 * q^39 + 9600 * q^40 + 28188 * q^41 - 173172 * q^43 - 44138 * q^44 + 21000 * q^45 + 17194 * q^46 + 54756 * q^47 + 191452 * q^48 + 5000 * q^50 - 20666 * q^51 + 131140 * q^52 - 55408 * q^53 - 106572 * q^54 - 52200 * q^55 - 103176 * q^57 + 56902 * q^58 - 13848 * q^59 - 66550 * q^60 + 71474 * q^61 - 426024 * q^62 + 362152 * q^64 + 75550 * q^65 + 25220 * q^66 + 38918 * q^67 - 760 * q^68 + 202956 * q^69 - 52736 * q^71 + 590150 * q^72 + 49316 * q^73 + 376230 * q^74 + 11250 * q^75 + 116028 * q^76 - 458768 * q^78 - 89006 * q^79 + 150400 * q^80 - 396558 * q^81 - 164222 * q^82 - 480036 * q^83 - 33500 * q^85 - 576468 * q^86 + 200182 * q^87 - 201656 * q^88 - 55030 * q^89 - 90900 * q^90 + 794444 * q^92 - 313224 * q^93 - 473094 * q^94 - 85900 * q^95 - 525292 * q^96 + 538584 * q^97 + 1428776 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)