Space of modular forms of level 441, weight 4, and Character 441.z

• Label: 441.4.z
• Level: $441$
• Weight: $4$
• Character orbit: 441.z
• Rep. character: $\chi_{441}(4,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $1992$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.z (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

	Total	New	Old
Modular forms	2040	2040	0
Cusp forms	1992	1992	0
Eisenstein series	48	48	0

Trace form

1992 * q - 8 * q^2 - 13 * q^3 + 648 * q^4 - 45 * q^5 - 22 * q^6 - 4 * q^8 - 195 * q^9 - 10 * q^10 - 5 * q^11 - 358 * q^12 + 7 * q^13 - 278 * q^14 - 25 * q^15 + 2544 * q^16 + 134 * q^17 - 148 * q^18 - 72 * q^19 + 355 * q^20 - 180 * q^21 + 11 * q^22 + 205 * q^23 - 428 * q^24 - 7905 * q^25 + 238 * q^26 - 328 * q^27 + 144 * q^28 - 341 * q^29 - 315 * q^30 - 54 * q^31 + 386 * q^32 - 37 * q^33 - 13 * q^34 - 317 * q^35 + 1490 * q^36 - 1118 * q^37 - 1417 * q^38 + 283 * q^39 - 43 * q^40 + 685 * q^41 - 353 * q^42 + 79 * q^43 + 479 * q^44 - 15 * q^45 - 3286 * q^46 + 74 * q^47 + 985 * q^48 + 270 * q^49 - 9 * q^50 + 1137 * q^51 + 667 * q^52 + 1850 * q^53 - 924 * q^54 - 1300 * q^55 - 7721 * q^56 + 1581 * q^57 - 1297 * q^58 + 1658 * q^59 + 6340 * q^60 + 5434 * q^61 - 1896 * q^62 - 507 * q^63 - 19332 * q^64 + 634 * q^65 + 4095 * q^66 - 288 * q^67 + 20086 * q^68 - 6863 * q^69 + 1037 * q^70 - 2890 * q^71 - 667 * q^72 + 310 * q^73 + 411 * q^74 + 5208 * q^75 - 1461 * q^76 + 2902 * q^77 + 5217 * q^78 + 342 * q^79 - 10877 * q^80 + 20497 * q^81 - 34 * q^82 + 1153 * q^83 - 8711 * q^84 - 130 * q^85 - 4713 * q^86 - 2060 * q^87 + 731 * q^88 - 2588 * q^89 - 285 * q^90 - 1580 * q^91 - 9853 * q^92 + 8242 * q^93 + 1184 * q^94 - 1445 * q^95 - 15717 * q^96 + 252 * q^97 + 9027 * q^98 - 7513 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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