Space of modular forms of level 280, weight 10, and Character 280.bg

• Label: 280.10.bg
• Level: $280$
• Weight: $10$
• Character orbit: 280.bg
• Rep. character: $\chi_{280}(9,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	280.bg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(280, [\chi])\).

	Total	New	Old
Modular forms	880	216	664
Cusp forms	848	216	632
Eisenstein series	32	0	32

Trace form

216 * q + 725486 * q^9 + 28462 * q^11 - 333268 * q^15 - 1257274 * q^19 + 2057510 * q^21 - 870642 * q^25 + 5816748 * q^29 - 6869916 * q^31 - 24317788 * q^35 - 43520044 * q^39 + 82741560 * q^41 + 31424632 * q^45 + 18723426 * q^49 + 28780704 * q^51 - 185816652 * q^55 - 489558480 * q^59 - 178377906 * q^61 + 297721414 * q^65 - 10376764 * q^69 + 475894864 * q^71 + 141312306 * q^75 + 136469492 * q^79 - 4151545764 * q^81 + 2463217396 * q^85 + 2255968398 * q^89 - 2523576436 * q^91 - 755879546 * q^95 + 3901972404 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(280, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)