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

• Label: 693.4.m
• Level: $693$
• Weight: $4$
• Character orbit: 693.m
• Rep. character: $\chi_{693}(64,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $360$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	1184	360	824
Cusp forms	1120	360	760
Eisenstein series	64	0	64

Trace form

360 * q - 2 * q^2 - 370 * q^4 + 8 * q^5 + 14 * q^7 - 106 * q^8 - 144 * q^10 - 44 * q^11 - 120 * q^13 + 105 * q^14 - 1506 * q^16 + 196 * q^17 - 222 * q^19 - 442 * q^20 + 248 * q^22 - 1036 * q^23 - 2286 * q^25 - 534 * q^26 + 175 * q^28 + 420 * q^29 - 256 * q^31 + 2640 * q^32 - 148 * q^34 - 280 * q^35 + 276 * q^37 + 1038 * q^38 - 1978 * q^40 - 460 * q^41 - 5776 * q^43 - 2745 * q^44 - 1999 * q^46 + 916 * q^47 - 4410 * q^49 - 2628 * q^50 - 242 * q^52 - 1176 * q^53 + 692 * q^55 - 462 * q^56 - 1825 * q^58 + 606 * q^59 + 984 * q^61 + 1498 * q^62 - 6994 * q^64 + 7400 * q^65 + 552 * q^67 + 4734 * q^68 + 756 * q^70 + 142 * q^71 + 3372 * q^73 - 934 * q^74 - 8812 * q^76 - 364 * q^77 - 1422 * q^79 - 3492 * q^80 + 2340 * q^82 - 11182 * q^83 + 7844 * q^85 - 2661 * q^86 - 4584 * q^88 - 1372 * q^89 - 756 * q^91 + 2795 * q^92 + 11230 * q^94 - 1508 * q^95 + 318 * q^97 + 882 * q^98

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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)