Space of modular forms of level 245, weight 10, and Character 245.j

• Label: 245.10.j
• Level: $245$
• Weight: $10$
• Character orbit: 245.j
• Rep. character: $\chi_{245}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $352$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(245, [\chi])\).

	Total	New	Old
Modular forms	520	368	152
Cusp forms	488	352	136
Eisenstein series	32	16	16

Trace form

352 * q + 44034 * q^4 - 283 * q^5 - 3768 * q^6 + 1087048 * q^9 + 35564 * q^10 - 5168 * q^11 + 546462 * q^15 - 11017530 * q^16 - 1617200 * q^19 - 384184 * q^20 - 1749444 * q^24 + 1236267 * q^25 + 751786 * q^26 + 12063212 * q^29 - 8218490 * q^30 + 7098286 * q^31 + 51405472 * q^34 + 611091180 * q^36 - 56395856 * q^39 + 19066822 * q^40 - 113748104 * q^41 + 92030918 * q^44 - 30552036 * q^45 + 168780318 * q^46 + 526723644 * q^50 - 132057618 * q^51 - 129445308 * q^54 - 5248810 * q^55 - 187049918 * q^59 - 4963648 * q^60 + 101573100 * q^61 - 7097279188 * q^64 + 271775598 * q^65 + 315370892 * q^66 + 2575884656 * q^69 + 1265186176 * q^71 + 796704546 * q^74 + 37268973 * q^75 - 5630456764 * q^76 + 1181657450 * q^79 - 722949872 * q^80 - 3670946560 * q^81 - 1066366946 * q^85 - 3388001676 * q^86 - 882280536 * q^89 + 9825416284 * q^90 - 765165090 * q^94 - 3352949935 * q^95 + 5845723236 * q^96 - 3830816748 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)