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

• Label: 560.3.bo
• Level: $560$
• Weight: $3$
• Character orbit: 560.bo
• Rep. character: $\chi_{560}(477,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.bo (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(288\)

Dimensions

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

	Total	New	Old
Modular forms	392	288	104
Cusp forms	376	288	88
Eisenstein series	16	0	16

Trace form

288 * q + 8 * q^4 + 864 * q^9 + 48 * q^12 - 56 * q^16 + 28 * q^18 + 64 * q^19 - 52 * q^22 + 96 * q^26 + 164 * q^30 + 80 * q^32 - 32 * q^34 + 96 * q^36 + 280 * q^38 - 264 * q^40 - 140 * q^42 - 312 * q^44 - 224 * q^46 + 256 * q^48 - 416 * q^50 + 192 * q^51 - 208 * q^52 + 352 * q^54 + 168 * q^56 - 276 * q^58 - 584 * q^60 + 64 * q^61 - 440 * q^62 - 352 * q^64 - 416 * q^66 - 776 * q^68 - 192 * q^69 - 160 * q^72 + 96 * q^73 + 32 * q^74 + 608 * q^75 - 512 * q^76 + 356 * q^78 + 944 * q^80 + 2592 * q^81 - 152 * q^82 - 320 * q^83 + 224 * q^86 - 200 * q^88 + 184 * q^90 + 168 * q^92 - 152 * q^94 + 544 * q^96 - 256 * q^99

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

\( S_{3}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)