Space of modular forms of level 343, weight 4, and Character 343.i

• Label: 343.4.i
• Level: $343$
• Weight: $4$
• Character orbit: 343.i
• Rep. character: $\chi_{343}(8,\cdot)$
• Character field: $\Q(\zeta_{49})$
• Dimension: $4074$
• Sturm bound: $130$

Defining parameters

Level:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	343.i (of order \(49\) and degree \(42\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 343 \)
Character field:			\(\Q(\zeta_{49})\)
Sturm bound:			\(130\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(343, [\chi])\).

	Total	New	Old
Modular forms	4158	4158	0
Cusp forms	4074	4074	0
Eisenstein series	84	84	0

Trace form

4074 * q - 42 * q^2 - 42 * q^3 - 42 * q^4 - 42 * q^5 - 70 * q^6 - 42 * q^7 - 42 * q^8 + 56 * q^9 - 42 * q^10 + 56 * q^11 - 427 * q^12 - 42 * q^13 - 217 * q^14 + 252 * q^15 - 42 * q^16 + 182 * q^17 - 84 * q^18 + 3108 * q^19 + 2646 * q^20 - 42 * q^21 + 546 * q^22 - 336 * q^23 - 672 * q^24 - 42 * q^25 + 490 * q^26 - 84 * q^27 - 168 * q^28 + 252 * q^29 - 35 * q^30 - 1337 * q^31 - 1218 * q^32 - 42 * q^33 + 770 * q^34 + 868 * q^35 + 798 * q^36 + 1624 * q^37 + 490 * q^38 + 1134 * q^39 + 1470 * q^40 + 70 * q^41 - 3430 * q^42 - 42 * q^43 + 938 * q^44 - 2786 * q^45 - 1806 * q^46 - 1106 * q^47 + 1981 * q^48 - 1386 * q^49 - 6209 * q^50 - 1218 * q^51 + 1246 * q^52 + 546 * q^53 - 1932 * q^54 + 17430 * q^55 + 2044 * q^56 + 1176 * q^57 + 15246 * q^58 - 10682 * q^59 + 112 * q^60 + 3052 * q^61 + 1890 * q^62 + 2856 * q^63 - 1610 * q^64 - 42 * q^65 + 2142 * q^66 - 35 * q^67 - 5747 * q^68 - 5502 * q^69 + 6132 * q^70 + 2800 * q^71 - 9345 * q^72 + 8022 * q^73 - 15330 * q^74 + 4116 * q^75 - 8085 * q^76 + 6510 * q^77 - 40614 * q^78 - 35 * q^79 + 903 * q^80 - 2688 * q^81 + 11053 * q^82 + 1806 * q^83 + 7847 * q^84 - 1218 * q^85 + 2261 * q^86 + 4004 * q^87 + 1771 * q^88 + 3178 * q^89 - 3584 * q^90 + 30128 * q^91 - 55902 * q^92 - 4949 * q^93 - 14637 * q^94 - 10388 * q^95 + 13027 * q^96 - 12621 * q^97 + 2303 * q^98 - 11011 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(343, [\chi])\) into newform subspaces

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