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

• Label: 693.4.cg
• Level: $693$
• Weight: $4$
• Character orbit: 693.cg
• Rep. character: $\chi_{693}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $944$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.cg (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
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	2368	976	1392
Cusp forms	2240	944	1296
Eisenstein series	128	32	96

Trace form

944 * q + 5 * q^2 - 477 * q^4 + 33 * q^5 - 60 * q^8 - 2 * q^11 + 146 * q^14 + 1711 * q^16 - 15 * q^17 - 15 * q^19 - 816 * q^22 + 200 * q^23 - 2785 * q^25 - 855 * q^26 - 370 * q^28 - 680 * q^29 - 1251 * q^31 + 520 * q^35 + 453 * q^37 + 1623 * q^38 - 2175 * q^40 + 276 * q^44 + 1370 * q^46 + 465 * q^47 + 1174 * q^49 - 1230 * q^50 - 15 * q^52 - 1905 * q^53 + 5096 * q^56 + 716 * q^58 + 2541 * q^59 - 2475 * q^61 + 15432 * q^64 + 1228 * q^67 + 255 * q^68 + 215 * q^70 + 6400 * q^71 + 2865 * q^73 + 915 * q^74 + 4341 * q^77 + 1195 * q^79 + 1065 * q^80 - 4569 * q^82 + 9020 * q^85 + 3602 * q^86 - 613 * q^88 - 6576 * q^89 - 144 * q^91 - 13938 * q^92 - 9255 * q^94 + 2115 * q^95

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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)