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

• Label: 693.4.ba
• Level: $693$
• Weight: $4$
• Character orbit: 693.ba
• Rep. character: $\chi_{693}(439,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $568$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	584	584	0
Cusp forms	568	568	0
Eisenstein series	16	16	0

Trace form

568 * q - 6 * q^3 + 1122 * q^4 + 30 * q^9 + 6 * q^11 - 6 * q^12 - 34 * q^14 + 6 * q^15 - 4366 * q^16 + 720 * q^20 + 14 * q^22 + 164 * q^23 - 13404 * q^25 - 204 * q^26 - 36 * q^27 - 6 * q^31 + 849 * q^33 - 48 * q^34 - 1332 * q^36 - 4 * q^37 + 1234 * q^42 - 459 * q^44 - 6 * q^45 - 6 * q^47 + 498 * q^48 - 2 * q^49 - 172 * q^53 + 592 * q^56 + 940 * q^58 + 1494 * q^59 - 1416 * q^60 - 33008 * q^64 + 2661 * q^66 + 2 * q^67 - 162 * q^69 + 208 * q^70 - 1232 * q^71 + 3564 * q^75 + 3083 * q^77 + 1262 * q^78 + 5748 * q^80 - 602 * q^81 + 36 * q^82 + 732 * q^86 + 1246 * q^88 + 4068 * q^89 + 1364 * q^91 + 2398 * q^92 + 5314 * q^93 + 2665 * 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.