Space of modular forms of level 693, weight 4, and Character 693.cj

• Label: 693.4.cj
• Level: $693$
• Weight: $4$
• Character orbit: 693.cj
• Rep. character: $\chi_{693}(20,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $2272$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.cj (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(693, [\chi])\).

	Total	New	Old
Modular forms	2336	2336	0
Cusp forms	2272	2272	0
Eisenstein series	64	64	0

Trace form

2272 * q - 18 * q^2 - 1126 * q^4 - 3 * q^7 + 84 * q^9 - 12 * q^11 - 9 * q^14 - 60 * q^15 + 4314 * q^16 + 244 * q^18 + 78 * q^21 + 24 * q^22 + 456 * q^23 + 6694 * q^25 - 236 * q^28 - 18 * q^29 - 156 * q^30 - 816 * q^32 + 652 * q^36 - 24 * q^37 + 2088 * q^39 - 315 * q^42 - 16 * q^43 - 120 * q^46 - 3 * q^49 + 888 * q^50 + 2044 * q^51 + 1914 * q^56 - 1012 * q^57 - 1454 * q^58 + 6578 * q^60 + 730 * q^63 + 32136 * q^64 - 1968 * q^65 - 16 * q^67 + 582 * q^70 - 2456 * q^72 + 78 * q^74 - 5268 * q^77 + 4072 * q^78 + 1434 * q^79 - 3500 * q^81 - 5271 * q^84 + 1214 * q^85 + 1182 * q^86 - 1304 * q^88 + 1360 * q^91 - 4038 * q^92 - 2528 * q^93 + 4674 * q^95 - 16714 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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