Space of modular forms of level 189, weight 6, and Character 189.bd

• Label: 189.6.bd
• Level: $189$
• Weight: $6$
• Character orbit: 189.bd
• Rep. character: $\chi_{189}(47,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $708$
• Sturm bound: $144$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 189 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(189, [\chi])\).

	Total	New	Old
Modular forms	732	732	0
Cusp forms	708	708	0
Eisenstein series	24	24	0

Trace form

708 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 360 * q^6 - 6 * q^7 - 18 * q^8 - 663 * q^9 - 9 * q^10 - 1143 * q^11 - 9 * q^12 + 3144 * q^14 - 744 * q^15 - 195 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 288 * q^20 - 8319 * q^21 - 12 * q^22 - 15918 * q^23 - 2196 * q^24 - 3 * q^25 - 12 * q^28 - 17922 * q^29 - 6573 * q^30 - 9 * q^31 - 11391 * q^32 - 9 * q^33 + 288 * q^34 - 9 * q^35 + 63018 * q^36 - 6 * q^37 - 9 * q^38 + 21087 * q^39 - 9 * q^40 + 43857 * q^42 - 12 * q^43 + 79641 * q^45 - 6 * q^46 - 84843 * q^47 + 10974 * q^49 + 67491 * q^50 - 21423 * q^51 - 9 * q^52 - 157905 * q^53 + 347121 * q^54 - 164661 * q^56 - 30294 * q^57 - 3 * q^58 - 9 * q^59 - 363255 * q^60 + 210321 * q^61 - 461439 * q^62 + 289083 * q^63 + 1277946 * q^64 - 11496 * q^65 + 103959 * q^66 - 3 * q^67 + 266904 * q^68 - 426492 * q^69 - 160323 * q^70 - 203454 * q^71 - 209289 * q^72 - 357081 * q^74 - 9 * q^75 - 9216 * q^76 + 491577 * q^77 + 389910 * q^78 - 108093 * q^79 - 294912 * q^80 - 795471 * q^81 - 18 * q^82 - 740790 * q^83 + 445785 * q^84 + 43713 * q^85 + 294411 * q^86 - 9 * q^87 + 98685 * q^88 - 9 * q^89 - 531441 * q^90 + 181995 * q^91 - 946272 * q^92 - 200463 * q^93 - 9 * q^94 - 267813 * q^95 - 9 * q^96 + 1307970 * q^98 + 254976 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

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