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

• Label: 693.4.bk
• Level: $693$
• Weight: $4$
• Character orbit: 693.bk
• Rep. character: $\chi_{693}(122,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $480$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
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	480	104
Cusp forms	568	480	88
Eisenstein series	16	0	16

Trace form

480 * q + 960 * q^4 - 12 * q^7 - 28 * q^9 - 72 * q^13 - 264 * q^14 + 260 * q^15 - 3840 * q^16 - 144 * q^17 + 108 * q^18 + 556 * q^21 + 288 * q^24 + 12000 * q^25 + 828 * q^27 + 192 * q^28 + 252 * q^29 - 2096 * q^30 - 360 * q^31 + 1380 * q^32 - 1152 * q^36 - 168 * q^37 + 1740 * q^38 + 1328 * q^39 + 1236 * q^41 + 600 * q^42 - 168 * q^43 - 612 * q^45 - 504 * q^46 + 396 * q^47 - 2640 * q^48 - 1032 * q^49 + 2256 * q^50 - 412 * q^51 - 1056 * q^53 - 3090 * q^54 - 1200 * q^56 - 3128 * q^57 + 932 * q^60 + 2412 * q^61 - 5904 * q^62 - 204 * q^63 - 30720 * q^64 - 264 * q^65 - 588 * q^67 - 14028 * q^68 - 1848 * q^69 + 360 * q^70 + 4296 * q^72 + 9352 * q^78 + 420 * q^79 - 8094 * q^80 - 2420 * q^81 + 3660 * q^83 + 14594 * q^84 + 4452 * q^89 + 19188 * q^90 + 900 * q^91 - 7734 * q^92 + 3312 * q^93 - 3528 * q^95 - 7002 * q^96 - 1584 * q^97 + 9078 * 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

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