Space of modular forms of level 1323, weight 2, and Character 1323.cf

• Label: 1323.2.cf
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.cf
• Rep. character: $\chi_{1323}(47,\cdot)$
• Character field: $\Q(\zeta_{126})$
• Dimension: $5976$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.cf (of order \(126\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1323 \)
Character field:			\(\Q(\zeta_{126})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

	Total	New	Old
Modular forms	6120	6120	0
Cusp forms	5976	5976	0
Eisenstein series	144	144	0

Trace form

5976 * q - 39 * q^2 - 33 * q^3 - 39 * q^4 - 33 * q^5 + 24 * q^6 - 36 * q^7 - 45 * q^8 - 39 * q^9 - 12 * q^10 - 39 * q^11 - 33 * q^12 - 42 * q^13 - 210 * q^14 - 30 * q^15 - 27 * q^16 - 54 * q^17 - 18 * q^18 - 54 * q^19 - 24 * q^20 - 57 * q^21 - 30 * q^22 - 111 * q^23 - 6 * q^24 - 39 * q^25 - 42 * q^27 - 72 * q^28 - 174 * q^29 - 18 * q^30 - 54 * q^31 - 51 * q^32 - 33 * q^33 - 60 * q^34 - 54 * q^35 - 294 * q^36 - 15 * q^37 - 75 * q^38 - 9 * q^39 - 33 * q^40 - 42 * q^41 + 267 * q^42 - 30 * q^43 - 63 * q^44 + 21 * q^45 - 15 * q^46 + 39 * q^47 - 72 * q^49 - 63 * q^50 - 75 * q^51 - 33 * q^52 + 270 * q^53 - 159 * q^54 - 84 * q^55 + 9 * q^56 - 30 * q^57 - 39 * q^58 - 33 * q^59 + 33 * q^60 + 21 * q^61 - 162 * q^62 - 9 * q^63 - 471 * q^64 - 18 * q^65 - 105 * q^66 - 18 * q^67 - 207 * q^68 - 438 * q^69 - 27 * q^70 - 45 * q^71 - 51 * q^72 - 21 * q^73 - 51 * q^74 + 219 * q^75 - 90 * q^76 + 15 * q^77 - 48 * q^78 - 18 * q^79 + 72 * q^80 - 39 * q^81 - 66 * q^82 - 132 * q^83 - 324 * q^84 - 15 * q^85 - 93 * q^86 - 33 * q^87 - 87 * q^88 - 54 * q^89 + 39 * q^90 + 90 * q^92 - 219 * q^93 - 33 * q^94 - 150 * q^95 - 789 * q^96 + 117 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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