Space of modular forms of level 736, weight 4, and Character 736.bf

• Label: 736.4.bf
• Level: $736$
• Weight: $4$
• Character orbit: 736.bf
• Rep. character: $\chi_{736}(13,\cdot)$
• Character field: $\Q(\zeta_{88})$
• Dimension: $11440$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	736.bf (of order \(88\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 736 \)
Character field:			\(\Q(\zeta_{88})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(736, [\chi])\).

	Total	New	Old
Modular forms	11600	11600	0
Cusp forms	11440	11440	0
Eisenstein series	160	160	0

Trace form

11440 * q - 36 * q^2 - 36 * q^3 - 36 * q^4 - 36 * q^5 - 36 * q^6 - 36 * q^7 - 36 * q^8 - 36 * q^9 - 276 * q^10 - 36 * q^11 - 36 * q^12 - 36 * q^13 - 36 * q^14 + 564 * q^16 + 324 * q^18 - 36 * q^19 - 36 * q^20 - 36 * q^21 + 392 * q^22 - 368 * q^23 - 992 * q^24 - 36 * q^25 - 76 * q^26 + 228 * q^27 - 796 * q^28 - 36 * q^29 - 100 * q^30 - 72 * q^31 - 36 * q^32 - 72 * q^33 - 100 * q^34 - 36 * q^35 - 1056 * q^36 - 36 * q^37 - 2016 * q^38 - 636 * q^39 + 1028 * q^40 - 36 * q^41 + 1324 * q^42 - 1652 * q^43 + 964 * q^44 - 296 * q^45 - 14440 * q^46 + 4852 * q^48 + 4228 * q^50 + 2724 * q^51 + 1692 * q^52 - 1540 * q^53 - 7812 * q^54 - 36 * q^55 - 2428 * q^56 - 36 * q^57 - 5256 * q^58 - 36 * q^59 - 548 * q^60 + 3612 * q^61 - 4856 * q^62 - 5112 * q^63 - 36 * q^64 - 72 * q^65 + 28 * q^66 - 4116 * q^67 - 2656 * q^68 + 1016 * q^69 - 872 * q^70 - 36 * q^71 + 288 * q^72 - 36 * q^73 + 2596 * q^74 - 1036 * q^75 + 10204 * q^76 + 17100 * q^77 + 2496 * q^78 + 6284 * q^80 + 12764 * q^82 - 36 * q^83 - 36 * q^84 - 1036 * q^85 + 1812 * q^86 - 36 * q^87 - 36 * q^88 - 36 * q^89 - 1764 * q^90 - 80 * q^91 - 10196 * q^92 + 136 * q^93 - 8676 * q^94 - 72 * q^95 - 23276 * q^96 - 72 * q^97 - 12204 * q^98 + 180 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(736, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.