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

• Label: 693.4.bx
• Level: $693$
• Weight: $4$
• Character orbit: 693.bx
• Rep. character: $\chi_{693}(4,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $2272$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.bx (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
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	2336	2336	0
Cusp forms	2272	2272	0
Eisenstein series	64	64	0

Trace form

2272 * q + 3 * q^2 - 3 * q^3 + 1123 * q^4 - 6 * q^5 + 4 * q^6 - 3 * q^7 + 8 * q^8 - 51 * q^9 + 16 * q^10 - 148 * q^12 - 6 * q^13 - 35 * q^14 + 102 * q^15 + 4339 * q^16 + 266 * q^17 - 147 * q^18 - 6 * q^19 + 274 * q^20 + 252 * q^21 + 8 * q^22 - 184 * q^23 - 157 * q^24 - 13406 * q^25 + 98 * q^26 + 6 * q^27 + 132 * q^28 - 422 * q^29 + 377 * q^30 + 3 * q^31 - 184 * q^32 + 772 * q^33 - 32 * q^34 + 628 * q^35 + 1344 * q^36 - 6 * q^37 - 650 * q^38 - 147 * q^39 + 1198 * q^40 + 586 * q^41 - 347 * q^42 - 16 * q^43 + 433 * q^44 + 1840 * q^45 - 54 * q^46 + 3 * q^47 + 56 * q^48 - 3 * q^49 + 625 * q^50 + 1565 * q^51 - 582 * q^52 + 1646 * q^53 - 1964 * q^54 + 830 * q^55 - 4926 * q^56 - 848 * q^57 - 1582 * q^58 + 503 * q^59 + 365 * q^60 + 3 * q^61 - 5632 * q^62 - 754 * q^63 - 32584 * q^64 + 1148 * q^65 - 3338 * q^66 + 8 * q^67 - 6950 * q^68 + 4227 * q^69 + 8 * q^70 - 680 * q^71 + 593 * q^72 - 6 * q^73 + 1106 * q^74 - 2149 * q^75 - 112 * q^76 + 224 * q^77 - 116 * q^78 - 681 * q^79 - 2674 * q^80 - 4583 * q^81 - 22 * q^82 + 3978 * q^83 - 1143 * q^84 - 976 * q^85 + 890 * q^86 - 2218 * q^87 + 728 * q^88 - 1376 * q^89 + 9676 * q^90 - 1384 * q^91 - 3752 * q^92 - 327 * q^93 - 61 * q^94 + 2119 * q^95 + 3603 * q^96 - 6 * q^97 - 8484 * q^98 - 2465 * 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.