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

• Label: 693.4.r
• Level: $693$
• Weight: $4$
• Character orbit: 693.r
• Rep. character: $\chi_{693}(32,\cdot)$
• 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.r (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 - 2 * q^3 - 1118 * q^4 + 30 * q^9 + 138 * q^12 - 6 * q^14 + 6 * q^15 - 4334 * q^16 - 60 * q^20 - 18 * q^22 - 13404 * q^25 + 288 * q^26 + 4 * q^27 + 2 * q^31 + 47 * q^33 + 12 * q^34 + 1060 * q^36 - 4 * q^37 + 114 * q^42 - 555 * q^44 + 2006 * q^45 - 6 * q^47 - 902 * q^48 - 2 * q^49 + 2184 * q^53 + 854 * q^55 - 6012 * q^56 + 1068 * q^58 + 1494 * q^59 + 4032 * q^60 + 32464 * q^64 - 1467 * q^66 + 2 * q^67 + 2366 * q^69 + 1644 * q^70 + 3340 * q^75 - 4419 * q^77 - 2866 * q^78 + 1980 * q^80 + 182 * q^81 + 12 * q^82 - 738 * q^88 + 4080 * q^89 - 1380 * q^91 - 102 * q^92 - 102 * q^93 - 4 * q^97 + 43 * 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.