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

• Label: 693.4.by
• Level: $693$
• Weight: $4$
• Character orbit: 693.by
• Rep. character: $\chi_{693}(37,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $944$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
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 + 451 * q^4 - 5 * q^5 - 12 * q^7 + 160 * q^8 - 224 * q^10 - 10 * q^11 - 116 * q^13 - 30 * q^14 + 1927 * q^16 + 65 * q^17 + 217 * q^19 + 436 * q^20 + 1356 * q^22 - 128 * q^23 + 3219 * q^25 + 75 * q^26 + 158 * q^28 - 384 * q^29 + 411 * q^31 + 480 * q^32 + 1680 * q^34 - 890 * q^35 + 117 * q^37 + 573 * q^38 + 1559 * q^40 - 536 * q^41 + 944 * q^43 - 2028 * q^44 - 58 * q^46 + 191 * q^47 + 1350 * q^49 - 1854 * q^50 - 111 * q^52 + 735 * q^53 + 1442 * q^55 - 8136 * q^56 - 56 * q^58 - 897 * q^59 + 225 * q^61 + 1040 * q^62 - 7016 * q^64 - 602 * q^65 - 1468 * q^67 + 321 * q^68 + 4539 * q^70 - 808 * q^71 - 3175 * q^73 - 269 * q^74 + 12800 * q^76 + 1111 * q^77 + 1305 * q^79 + 1977 * q^80 + 3565 * q^82 + 3148 * q^83 - 7960 * q^85 - 4800 * q^86 - 365 * q^88 - 4280 * q^89 + 3300 * q^91 + 10642 * q^92 + 809 * q^94 + 329 * q^95 - 3216 * q^97 - 5124 * 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

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