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

• Label: 693.4.i
• Level: $693$
• Weight: $4$
• Character orbit: 693.i
• Rep. character: $\chi_{693}(100,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $200$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
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	592	200	392
Cusp forms	560	200	360
Eisenstein series	32	0	32

Trace form

200 * q - 400 * q^4 - 20 * q^5 + 20 * q^7 + 84 * q^8 - 6 * q^10 - 248 * q^13 - 396 * q^14 - 1628 * q^16 + 48 * q^17 - 116 * q^19 + 1136 * q^20 + 192 * q^23 - 2436 * q^25 - 746 * q^26 + 576 * q^28 + 360 * q^29 + 312 * q^31 - 1356 * q^32 - 1448 * q^34 + 768 * q^35 - 560 * q^37 - 64 * q^38 + 1020 * q^40 + 952 * q^41 + 1320 * q^43 + 308 * q^44 + 26 * q^46 - 696 * q^47 + 224 * q^49 - 4104 * q^50 + 658 * q^52 - 88 * q^53 - 880 * q^55 + 1266 * q^56 - 2146 * q^58 - 1144 * q^59 + 892 * q^61 + 2068 * q^62 + 12252 * q^64 - 312 * q^65 + 1412 * q^67 + 740 * q^68 - 4374 * q^70 - 56 * q^71 + 724 * q^73 - 2612 * q^74 + 2744 * q^76 - 88 * q^77 + 2056 * q^79 - 174 * q^80 + 1798 * q^82 + 7264 * q^83 - 1920 * q^85 + 5118 * q^86 + 396 * q^88 - 1196 * q^89 - 236 * q^91 - 1532 * q^92 - 4074 * q^94 + 2476 * q^95 - 4584 * q^97 - 1938 * 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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)