Space of modular forms of level 560, weight 3, and Character 560.ck

• Label: 560.3.ck
• Level: $560$
• Weight: $3$
• Character orbit: 560.ck
• Rep. character: $\chi_{560}(177,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $184$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.ck (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(560, [\chi])\).

	Total	New	Old
Modular forms	816	200	616
Cusp forms	720	184	536
Eisenstein series	96	16	80

Trace form

184 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 + 8 * q^15 - 2 * q^17 - 24 * q^21 - 46 * q^23 - 2 * q^25 + 44 * q^27 + 4 * q^31 - 14 * q^33 + 52 * q^35 - 2 * q^37 - 48 * q^41 + 8 * q^43 - 102 * q^45 + 98 * q^47 - 188 * q^51 - 2 * q^53 - 92 * q^55 - 108 * q^57 - 4 * q^61 + 228 * q^63 - 98 * q^65 - 142 * q^67 - 304 * q^71 - 226 * q^73 + 2 * q^75 + 94 * q^77 + 520 * q^81 - 376 * q^83 - 8 * q^85 - 16 * q^87 + 584 * q^91 + 130 * q^93 + 198 * q^95 - 40 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)