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

• Label: 459.3.bc
• Level: $459$
• Weight: $3$
• Character orbit: 459.bc
• Rep. character: $\chi_{459}(7,\cdot)$
• Character field: $\Q(\zeta_{144})$
• Dimension: $5088$
• Sturm bound: $162$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.bc (of order \(144\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 459 \)
Character field:			\(\Q(\zeta_{144})\)
Sturm bound:			\(162\)

Dimensions

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

	Total	New	Old
Modular forms	5280	5280	0
Cusp forms	5088	5088	0
Eisenstein series	192	192	0

Trace form

5088 * q - 48 * q^2 - 48 * q^3 - 48 * q^4 - 48 * q^5 - 48 * q^6 - 48 * q^7 - 24 * q^8 - 48 * q^9 - 24 * q^10 - 48 * q^11 - 336 * q^12 - 48 * q^13 - 48 * q^14 - 48 * q^15 - 24 * q^17 - 96 * q^18 - 24 * q^19 - 48 * q^20 - 768 * q^21 - 48 * q^22 - 48 * q^23 - 48 * q^24 - 48 * q^25 - 96 * q^26 - 48 * q^27 - 96 * q^28 - 48 * q^29 - 48 * q^30 - 48 * q^31 - 48 * q^32 - 48 * q^34 - 48 * q^35 - 48 * q^36 - 24 * q^37 + 528 * q^38 - 48 * q^39 - 48 * q^40 - 48 * q^41 - 48 * q^42 + 672 * q^43 - 24 * q^44 - 48 * q^45 - 24 * q^46 - 408 * q^47 - 48 * q^48 - 48 * q^49 - 48 * q^51 - 96 * q^52 - 96 * q^53 - 48 * q^54 - 96 * q^55 + 1392 * q^56 - 48 * q^57 - 48 * q^58 - 48 * q^59 + 4320 * q^60 - 48 * q^61 - 24 * q^62 - 48 * q^63 - 24 * q^64 - 1488 * q^65 - 48 * q^66 - 48 * q^68 + 480 * q^69 + 48 * q^70 - 24 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^74 - 48 * q^75 - 48 * q^76 - 48 * q^77 + 3384 * q^78 - 48 * q^79 - 96 * q^80 - 48 * q^81 - 96 * q^82 - 48 * q^83 - 48 * q^85 - 3696 * q^86 - 48 * q^87 - 48 * q^88 - 24 * q^89 - 48 * q^90 - 24 * q^91 - 48 * q^92 - 48 * q^93 - 48 * q^94 - 1488 * q^95 - 48 * q^96 - 48 * q^97 - 24 * q^98 + 1776 * 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.