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

• Label: 693.4.w
• Level: $693$
• Weight: $4$
• Character orbit: 693.w
• Rep. character: $\chi_{693}(428,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $432$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
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	432	152
Cusp forms	568	432	136
Eisenstein series	16	0	16

Trace form

432 * q - 864 * q^4 + 24 * q^5 + 92 * q^9 + 138 * q^11 - 160 * q^12 + 184 * q^15 - 3456 * q^16 - 384 * q^20 + 36 * q^22 + 5256 * q^25 - 1800 * q^27 + 36 * q^31 - 254 * q^33 - 360 * q^34 + 1488 * q^36 + 144 * q^37 + 1416 * q^38 - 156 * q^45 - 2328 * q^47 + 1728 * q^48 + 10584 * q^49 + 936 * q^59 + 3172 * q^60 + 27648 * q^64 + 1494 * q^66 + 936 * q^67 - 804 * q^69 + 3016 * q^75 - 1480 * q^78 - 668 * q^81 - 4176 * q^82 + 3672 * q^86 - 1656 * q^88 + 1008 * q^91 + 18924 * q^92 + 6016 * q^93 + 1044 * q^97 + 3048 * 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.

Decomposition of \(S_{4}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)