Space of modular forms of level 1323, weight 4, and Character 1323.ce

• Label: 1323.4.ce
• Level: $1323$
• Weight: $4$
• Character orbit: 1323.ce
• Rep. character: $\chi_{1323}(20,\cdot)$
• Character field: $\Q(\zeta_{126})$
• Dimension: $18072$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1323.ce (of order \(126\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1323 \)
Character field:			\(\Q(\zeta_{126})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

	Total	New	Old
Modular forms	18216	18216	0
Cusp forms	18072	18072	0
Eisenstein series	144	144	0

Trace form

18072 * q - 30 * q^2 - 42 * q^3 - 30 * q^4 - 42 * q^5 + 42 * q^6 - 36 * q^7 - 45 * q^8 - 30 * q^9 - 21 * q^10 - 30 * q^11 - 42 * q^12 - 42 * q^13 - 354 * q^14 - 30 * q^15 + 18 * q^16 - 63 * q^17 - 72 * q^18 - 42 * q^20 + 96 * q^21 - 30 * q^22 - 1290 * q^23 - 42 * q^24 - 30 * q^25 - 42 * q^27 - 72 * q^28 - 660 * q^29 + 1098 * q^30 + 354 * q^32 - 42 * q^33 - 42 * q^34 + 1188 * q^35 + 390 * q^36 - 15 * q^37 - 210 * q^38 - 450 * q^39 - 42 * q^40 - 42 * q^41 + 3066 * q^42 - 30 * q^43 - 45 * q^44 - 42 * q^45 - 15 * q^46 + 2730 * q^47 - 630 * q^49 + 1350 * q^50 - 1452 * q^51 - 42 * q^52 - 42 * q^54 - 84 * q^55 + 7173 * q^56 + 4605 * q^57 - 30 * q^58 - 42 * q^59 + 5298 * q^60 - 42 * q^61 - 63 * q^62 - 36 * q^63 - 93711 * q^64 + 2322 * q^65 - 42 * q^66 - 72 * q^67 - 16422 * q^69 + 2097 * q^70 - 45 * q^71 + 1362 * q^72 - 21 * q^73 - 2598 * q^74 - 15288 * q^75 - 1386 * q^76 - 7716 * q^77 + 294 * q^78 - 72 * q^79 - 30 * q^81 - 84 * q^82 - 42 * q^83 - 19377 * q^84 - 780 * q^85 - 8346 * q^86 - 42 * q^87 + 3090 * q^88 - 63 * q^89 - 42 * q^90 - 288 * q^91 - 44010 * q^92 + 13830 * q^93 - 42 * q^94 - 8961 * q^95 - 17808 * q^96 - 45963 * q^98 + 23112 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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