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

• Label: 693.4.j
• Level: $693$
• Weight: $4$
• Character orbit: 693.j
• Rep. character: $\chi_{693}(232,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $360$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	584	360	224
Cusp forms	568	360	208
Eisenstein series	16	0	16

Trace form

360 * q - 4 * q^3 - 720 * q^4 - 8 * q^5 - 60 * q^6 + 24 * q^8 + 32 * q^9 - 88 * q^11 - 376 * q^12 - 112 * q^14 + 48 * q^15 - 2880 * q^16 + 1308 * q^18 + 180 * q^20 - 424 * q^23 + 988 * q^24 - 4356 * q^25 - 2640 * q^26 - 856 * q^27 + 224 * q^30 + 36 * q^31 + 364 * q^32 - 352 * q^33 - 792 * q^34 - 224 * q^36 + 144 * q^37 + 2408 * q^38 + 480 * q^39 - 360 * q^40 + 512 * q^41 - 280 * q^42 + 1760 * q^44 + 868 * q^45 - 144 * q^46 - 16 * q^47 - 776 * q^48 - 8820 * q^49 + 2620 * q^50 - 856 * q^51 + 1836 * q^52 + 1160 * q^53 - 2708 * q^54 + 792 * q^55 - 1344 * q^56 + 1048 * q^57 + 1188 * q^58 - 1668 * q^59 + 1868 * q^60 + 2664 * q^62 + 952 * q^63 + 19224 * q^64 + 1336 * q^65 - 612 * q^67 + 1352 * q^68 - 1844 * q^69 + 6392 * q^71 + 5468 * q^72 - 2408 * q^74 + 10404 * q^75 + 2232 * q^76 - 616 * q^77 - 4560 * q^78 - 2368 * q^80 + 2536 * q^81 + 10296 * q^82 + 1184 * q^83 - 980 * q^84 - 3312 * q^85 - 5820 * q^86 - 2112 * q^87 + 2960 * q^89 - 9996 * q^90 - 2568 * q^92 - 10008 * q^93 - 2700 * q^94 + 3944 * q^95 - 436 * q^96 - 2736 * q^97 + 220 * 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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)