Space of modular forms of level 441, weight 6, and Character 441.z

• Label: 441.6.z
• Level: $441$
• Weight: $6$
• Character orbit: 441.z
• Rep. character: $\chi_{441}(4,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $3336$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	441.z (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(441, [\chi])\).

	Total	New	Old
Modular forms	3384	3384	0
Cusp forms	3336	3336	0
Eisenstein series	48	48	0

Trace form

3336 * q - 8 * q^2 - 13 * q^3 + 4408 * q^4 + 195 * q^5 - 178 * q^6 - 35 * q^7 + 44 * q^8 + 2457 * q^9 + 38 * q^10 - 5 * q^11 + 2162 * q^12 - 186 * q^13 - 6170 * q^14 + 776 * q^15 + 69592 * q^16 - 2071 * q^17 + 4436 * q^18 + 50 * q^19 - 2789 * q^20 + 3558 * q^21 + 59 * q^22 + 160 * q^23 + 1708 * q^24 - 337505 * q^25 - 4826 * q^26 - 8554 * q^27 - 824 * q^28 + 47755 * q^29 - 6735 * q^30 - 1078 * q^31 - 3070 * q^32 + 9476 * q^33 - 37 * q^34 + 24328 * q^35 - 68782 * q^36 - 33553 * q^37 + 44951 * q^38 - 17222 * q^39 + 2021 * q^40 - 46637 * q^41 + 53251 * q^42 - 9249 * q^43 - 7129 * q^44 - 45255 * q^45 + 123278 * q^46 - 166726 * q^47 + 111601 * q^48 - 9785 * q^49 + 9759 * q^50 - 28686 * q^51 - 62149 * q^52 - 283342 * q^53 - 114792 * q^54 + 77660 * q^55 + 964879 * q^56 + 31473 * q^57 + 24947 * q^58 - 93397 * q^59 + 103420 * q^60 - 298687 * q^61 + 301464 * q^62 - 100830 * q^63 - 2160596 * q^64 - 11615 * q^65 + 107751 * q^66 + 629 * q^67 - 1276634 * q^68 + 78550 * q^69 + 19301 * q^70 - 137431 * q^71 + 136301 * q^72 + 41988 * q^73 + 263715 * q^74 - 342051 * q^75 - 4165 * q^76 + 14389 * q^77 - 335295 * q^78 - 23479 * q^79 + 1063915 * q^80 - 721451 * q^81 - 58 * q^82 - 835559 * q^83 + 2475193 * q^84 - 3130 * q^85 - 44793 * q^86 - 330887 * q^87 + 61307 * q^88 - 123440 * q^89 + 86883 * q^90 + 21423 * q^91 + 245003 * q^92 + 413875 * q^93 - 96376 * q^94 - 269 * q^95 + 885363 * q^96 + 34667 * q^97 + 1364595 * q^98 + 1035014 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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