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

• Label: 693.4.cq
• Level: $693$
• Weight: $4$
• Character orbit: 693.cq
• Rep. character: $\chi_{693}(29,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $1728$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.cq (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
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	1728	608
Cusp forms	2272	1728	544
Eisenstein series	64	0	64

Trace form

1728 * q + 864 * q^4 - 24 * q^5 + 100 * q^6 + 68 * q^9 - 138 * q^11 - 160 * q^12 - 84 * q^15 + 3456 * q^16 - 920 * q^18 - 900 * q^19 + 384 * q^20 - 36 * q^22 - 1200 * q^24 - 5256 * q^25 + 1800 * q^27 + 1800 * q^29 + 1560 * q^30 - 36 * q^31 + 2264 * q^33 + 360 * q^34 + 952 * q^36 - 144 * q^37 - 1056 * q^38 + 1540 * q^39 - 5184 * q^45 + 2328 * q^47 - 1728 * q^48 - 10584 * q^49 - 930 * q^51 - 8340 * q^57 + 3894 * q^59 - 3172 * q^60 - 27648 * q^64 + 6956 * q^66 - 3996 * q^67 + 23010 * q^68 + 5044 * q^69 + 3450 * q^72 - 4766 * q^75 + 7400 * q^78 + 4828 * q^81 - 6264 * q^82 + 12780 * q^83 + 8960 * q^84 + 8508 * q^86 - 8784 * q^88 - 5200 * q^90 + 1512 * q^91 - 18924 * q^92 - 3036 * q^93 - 10320 * q^95 - 29440 * q^96 - 1314 * q^97 - 3248 * 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

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