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

• Label: 693.4.cb
• Level: $693$
• Weight: $4$
• Character orbit: 693.cb
• Rep. character: $\chi_{693}(74,\cdot)$
• 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.cb (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 - 3 * q^3 - 2246 * q^4 - 9 * q^5 - 20 * q^6 - 5 * q^7 + 45 * q^9 + 224 * q^12 - 10 * q^13 - 9 * q^14 - 126 * q^15 - 8678 * q^16 - 5 * q^18 - 10 * q^19 - 90 * q^20 + 8 * q^22 + 228 * q^23 + 155 * q^24 - 6697 * q^25 - 312 * q^26 + 6 * q^27 - 20 * q^28 - 30 * q^29 - 275 * q^30 - 6 * q^31 - 1382 * q^33 - 32 * q^34 - 1950 * q^35 - 1080 * q^36 - 6 * q^37 + 957 * q^38 + 915 * q^39 + 645 * q^40 - 30 * q^41 + 499 * q^42 - 555 * q^44 + 1116 * q^45 + 70 * q^46 + 3092 * q^48 - 3 * q^49 - 1905 * q^50 + 1035 * q^51 + 5 * q^52 - 3276 * q^53 - 894 * q^55 + 2082 * q^56 - 300 * q^57 - 721 * q^58 - 2105 * q^60 - 10 * q^61 + 3120 * q^63 - 32584 * q^64 - 2389 * q^66 - 16 * q^67 - 15 * q^68 - 4251 * q^69 - 1473 * q^70 + 6715 * q^72 - 10 * q^73 - 15 * q^74 - 2327 * q^75 + 1164 * q^77 - 7644 * q^78 - 10 * q^79 + 1980 * q^80 + 3581 * q^81 - 22 * q^82 - 30 * q^83 - 1600 * q^84 - 10 * q^85 + 1191 * q^86 - 364 * q^88 + 4080 * q^89 - 15750 * q^90 + 1360 * q^91 - 10008 * q^92 + 3049 * q^93 - 10 * q^94 + 7125 * q^96 - 6 * q^97 - 7903 * 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.