Space of modular forms of level 1100, weight 6, and Character 1100.bt

• Label: 1100.6.bt
• Level: $1100$
• Weight: $6$
• Character orbit: 1100.bt
• Rep. character: $\chi_{1100}(211,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $3584$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1100.bt (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1100 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1100, [\chi])\).

	Total	New	Old
Modular forms	3616	3616	0
Cusp forms	3584	3584	0
Eisenstein series	32	32	0

Trace form

3584 * q - 5 * q^2 - q^4 - 6 * q^5 - 5 * q^6 - 5 * q^8 + 71926 * q^9 - 1420 * q^10 - 1374 * q^12 - 10 * q^13 - 33 * q^14 - 1277 * q^16 - 10 * q^17 - 1225 * q^18 + 2040 * q^20 + 2563 * q^22 - 10 * q^24 - 4098 * q^25 + 12846 * q^26 - 10 * q^29 + 155 * q^30 + 13170 * q^33 + 26 * q^34 + 4338 * q^36 - 2 * q^37 - 37301 * q^38 + 21030 * q^40 + 29998 * q^42 - 7277 * q^44 - 6500 * q^45 - 5 * q^46 + 1452 * q^48 - 2102880 * q^49 + 85710 * q^50 - 98025 * q^52 + 58282 * q^53 - 38880 * q^54 + 67222 * q^56 - 20 * q^57 + 105798 * q^58 - 125500 * q^60 - 10 * q^61 - 193105 * q^62 - 2845 * q^64 - 110943 * q^66 + 248265 * q^68 - 215750 * q^69 + 22025 * q^70 - 30475 * q^74 - 582864 * q^77 - 144490 * q^78 - 182352 * q^80 - 5668220 * q^81 + 367830 * q^82 + 81600 * q^84 - 10 * q^85 + 31387 * q^86 + 149187 * q^88 - 12 * q^89 - 743950 * q^90 - 708596 * q^92 - 269058 * q^93 - 53270 * q^94 - 252115 * q^96 + 165218 * q^97 + 567735 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

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