Space of modular forms of level 1089, weight 6, and Character 1089.y

• Label: 1089.6.y
• Level: $1089$
• Weight: $6$
• Character orbit: 1089.y
• Rep. character: $\chi_{1089}(32,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $13160$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1089.y (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1089 \)
Character field:			\(\Q(\zeta_{66})\)
Sturm bound:			\(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1089, [\chi])\).

	Total	New	Old
Modular forms	13240	13240	0
Cusp forms	13160	13160	0
Eisenstein series	80	80	0

Trace form

13160 * q - 33 * q^2 - 62 * q^3 + 10487 * q^4 - 27 * q^5 - 374 * q^6 - 11 * q^7 - 414 * q^9 - 44 * q^10 + 87 * q^11 - 7399 * q^12 - 11 * q^13 - 27 * q^14 + 2745 * q^15 + 166967 * q^16 - 374 * q^18 - 44 * q^19 - 219 * q^20 + 2651 * q^21 + 874 * q^22 + 171 * q^23 + 49764 * q^24 - 406259 * q^25 + 1258 * q^27 - 44 * q^28 - 33 * q^29 - 5368 * q^30 - 9 * q^31 - 33 * q^32 + 18009 * q^33 + 7711 * q^34 + 158 * q^36 - 36 * q^37 - 186603 * q^38 + 2651 * q^39 - 33 * q^41 + 96861 * q^42 - 11 * q^43 - 64773 * q^45 - 44 * q^46 - 27 * q^47 + 21261 * q^48 - 1551055 * q^49 - 33 * q^50 + 41734 * q^51 - 11 * q^52 - 848914 * q^54 - 22362 * q^55 + 243843 * q^56 - 301895 * q^57 + 9895 * q^58 + 126033 * q^59 - 194501 * q^60 - 11 * q^61 - 49390 * q^63 - 5279908 * q^64 - 33 * q^65 + 47875 * q^66 + 21045 * q^67 - 33 * q^68 - 149451 * q^69 + 32269 * q^70 + 720874 * q^72 - 44 * q^73 - 33 * q^74 + 173045 * q^75 + 236005 * q^76 - 287547 * q^77 - 22880 * q^78 - 11 * q^79 + 291218 * q^81 - 111572 * q^82 - 33 * q^83 - 5368 * q^84 - 97361 * q^85 - 378867 * q^86 - 2695 * q^87 - 334526 * q^88 - 2865500 * q^90 - 223868 * q^91 - 634149 * q^92 - 586232 * q^93 + 1726791 * q^95 - 2695 * q^96 + 174429 * q^97 - 723648 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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