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

• Label: 560.3.bg
• Level: $560$
• Weight: $3$
• Character orbit: 560.bg
• Rep. character: $\chi_{560}(211,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $192$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.bg (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
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	192	200
Cusp forms	376	192	184
Eisenstein series	16	0	16

Trace form

192 * q - 12 * q^4 - 24 * q^6 + 40 * q^10 - 32 * q^11 + 120 * q^12 + 28 * q^14 - 76 * q^16 - 60 * q^18 + 64 * q^19 + 36 * q^22 + 128 * q^23 - 40 * q^24 + 96 * q^26 + 192 * q^27 - 32 * q^29 - 40 * q^32 - 32 * q^34 + 168 * q^36 + 96 * q^37 - 768 * q^39 - 96 * q^43 - 52 * q^44 + 288 * q^46 + 1344 * q^49 - 20 * q^50 + 192 * q^51 - 320 * q^52 + 160 * q^53 + 288 * q^54 + 28 * q^56 + 100 * q^58 + 576 * q^59 + 64 * q^61 - 312 * q^62 - 468 * q^64 + 416 * q^66 - 160 * q^67 - 552 * q^68 - 192 * q^69 - 892 * q^72 - 396 * q^74 - 1024 * q^76 - 224 * q^77 + 1136 * q^78 + 480 * q^80 - 1728 * q^81 + 392 * q^82 - 320 * q^85 + 708 * q^86 + 300 * q^88 - 432 * q^92 - 192 * q^93 - 280 * q^94 + 176 * q^96 - 736 * 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

\( S_{3}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)