Space of modular forms of level 560, weight 6, and Character 560.ch

• Label: 560.6.ch
• Level: $560$
• Weight: $6$
• Character orbit: 560.ch
• Rep. character: $\chi_{560}(117,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1904$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	560.ch (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 560 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(560, [\chi])\).

	Total	New	Old
Modular forms	1936	1936	0
Cusp forms	1904	1904	0
Eisenstein series	32	32	0

Trace form

1904 * q - 2 * q^2 - 6 * q^5 - 500 * q^8 - 75816 * q^9 - 6 * q^10 - 4 * q^11 - 6 * q^12 - 16 * q^15 - 4 * q^16 - 12 * q^17 - 360 * q^18 - 8 * q^21 - 136 * q^22 + 2916 * q^24 - 12 * q^26 + 21230 * q^28 + 19926 * q^30 - 24 * q^31 - 4822 * q^32 - 12 * q^33 + 8634 * q^35 + 8176 * q^36 - 41244 * q^38 - 1944 * q^39 - 107616 * q^40 - 16466 * q^42 - 16 * q^43 + 43320 * q^44 + 1452 * q^45 - 4 * q^46 - 12 * q^47 - 8 * q^50 - 4 * q^51 - 80724 * q^52 - 4 * q^53 - 384 * q^54 - 8 * q^56 + 1944 * q^57 + 125302 * q^58 + 43440 * q^59 + 84840 * q^60 - 12 * q^61 + 67220 * q^63 - 4 * q^65 - 191172 * q^66 + 89252 * q^67 + 291780 * q^68 + 248472 * q^70 - 20116 * q^72 + 166204 * q^74 - 6 * q^75 - 67236 * q^77 + 80728 * q^78 - 492600 * q^80 - 5826176 * q^81 + 377142 * q^82 + 654012 * q^84 + 12492 * q^85 + 130836 * q^86 + 2916 * q^87 - 450692 * q^88 - 164728 * q^91 - 342196 * q^92 + 766440 * q^94 - 38428 * q^95 - 12 * q^96 + 360026 * q^98 + 1944 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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