Space of modular forms of level 459, weight 3, and Character 459.bb

• Label: 459.3.bb
• Level: $459$
• Weight: $3$
• Character orbit: 459.bb
• Rep. character: $\chi_{459}(2,\cdot)$
• Character field: $\Q(\zeta_{72})$
• Dimension: $2544$
• Sturm bound: $162$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.bb (of order \(72\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 459 \)
Character field:			\(\Q(\zeta_{72})\)
Sturm bound:			\(162\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(459, [\chi])\).

	Total	New	Old
Modular forms	2640	2640	0
Cusp forms	2544	2544	0
Eisenstein series	96	96	0

Trace form

2544 * q - 24 * q^2 - 24 * q^3 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9 - 12 * q^10 + 48 * q^11 + 120 * q^12 - 24 * q^14 - 24 * q^15 - 48 * q^16 - 36 * q^17 - 48 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^22 - 240 * q^23 - 444 * q^24 - 24 * q^25 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^31 + 168 * q^32 - 48 * q^33 - 24 * q^34 - 72 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^39 - 216 * q^40 - 24 * q^41 - 1344 * q^42 - 384 * q^43 - 36 * q^44 - 24 * q^45 - 12 * q^46 - 24 * q^48 - 24 * q^49 - 48 * q^50 - 24 * q^51 - 48 * q^52 + 552 * q^54 - 744 * q^56 + 480 * q^57 - 24 * q^58 + 984 * q^59 - 1920 * q^60 - 24 * q^61 - 36 * q^62 + 1416 * q^63 + 696 * q^65 + 876 * q^66 - 48 * q^67 + 168 * q^68 - 336 * q^69 - 72 * q^70 - 1332 * q^71 - 12 * q^73 - 528 * q^74 - 24 * q^75 - 216 * q^76 - 564 * q^77 - 2124 * q^78 - 24 * q^79 - 48 * q^82 - 1464 * q^83 - 48 * q^84 - 24 * q^85 + 1752 * q^86 - 24 * q^87 + 1704 * q^88 - 252 * q^90 - 12 * q^91 - 24 * q^92 - 24 * q^93 - 24 * q^94 + 2136 * q^95 - 3456 * q^96 + 1056 * q^97 - 1032 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(459, [\chi])\) into newform subspaces

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