Space of modular forms of level 144, weight 14, and Character 144.x

• Label: 144.14.x
• Level: $144$
• Weight: $14$
• Character orbit: 144.x
• Rep. character: $\chi_{144}(13,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1240$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(144, [\chi])\).

	Total	New	Old
Modular forms	1256	1256	0
Cusp forms	1240	1240	0
Eisenstein series	16	16	0

Trace form

1240 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 255050 * q^6 - 8 * q^8 - 8 * q^10 - 2 * q^11 - 25472296 * q^12 - 2 * q^13 - 32770 * q^14 - 8 * q^15 - 2 * q^16 - 16 * q^17 + 139499622 * q^18 - 8 * q^19 - 249890748 * q^20 - 3188650 * q^21 - 2 * q^22 + 2570025848 * q^24 + 7637288216 * q^26 + 2071888424 * q^27 - 268435464 * q^28 - 2 * q^29 + 17615970366 * q^30 - 4 * q^31 - 29075074582 * q^32 - 8 * q^33 - 16386 * q^34 - 4882812508 * q^35 + 10254557534 * q^36 - 8 * q^37 - 43160672494 * q^38 - 2 * q^40 - 146152415236 * q^42 - 2 * q^43 - 322692899724 * q^44 - 2441406254 * q^45 + 191352196736 * q^46 - 431168613164 * q^47 - 45395117278 * q^48 + 8249407171792 * q^49 + 388656625464 * q^50 + 312814444284 * q^51 - 2 * q^52 - 8 * q^53 + 1492524361766 * q^54 - 591132527948 * q^56 + 258478673056 * q^58 + 496186348330 * q^59 - 65422333362 * q^60 - 2 * q^61 - 2057753676860 * q^62 - 387556041636 * q^63 - 2537654071724 * q^64 - 4 * q^65 - 4806511312396 * q^66 - 2 * q^67 - 1888424312096 * q^68 - 3188650 * q^69 + 193778020812 * q^70 + 11167064970882 * q^72 - 3035394474814 * q^74 - 10177058794504 * q^75 - 197339008166 * q^76 - 387556041630 * q^77 + 11304362241052 * q^78 - 4 * q^79 + 45029074532112 * q^80 - 8 * q^81 + 8136005194460 * q^82 + 8662557183818 * q^83 + 3866321434394 * q^84 - 2441406252 * q^85 + 36020446154710 * q^86 - 8585312535386 * q^88 + 5324751773496 * q^90 - 387556041636 * q^91 + 10577346205264 * q^92 - 3412032366934 * q^93 + 32766 * q^94 + 47045880999996 * q^95 + 34910424716854 * q^96 - 4 * q^97 - 24489992950376 * q^98 - 31916503509686 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

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