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

• Label: 280.10.bo
• Level: $280$
• Weight: $10$
• Character orbit: 280.bo
• Rep. character: $\chi_{280}(17,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $432$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

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

	Total	New	Old
Modular forms	1760	432	1328
Cusp forms	1696	432	1264
Eisenstein series	64	0	64

Trace form

432 * q + 9756 * q^7 - 56924 * q^11 - 77112 * q^15 - 2212516 * q^21 + 5565116 * q^23 + 2885112 * q^25 - 11550276 * q^33 + 3084504 * q^35 + 19596168 * q^37 + 25967984 * q^43 - 188547792 * q^45 + 116779416 * q^51 - 105557744 * q^53 - 198320096 * q^57 - 73366884 * q^61 + 899231292 * q^63 - 302339508 * q^65 - 146691216 * q^67 - 1344542656 * q^71 + 739614672 * q^73 + 1617559632 * q^75 + 1312822564 * q^77 + 8352952800 * q^81 + 2987811480 * q^85 - 1784476332 * q^87 + 6017388080 * q^91 + 1248947520 * q^93 - 569560296 * q^95

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

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