Space of modular forms of level 1058, weight 4, and Character 1058.e

• Label: 1058.4.e
• Level: $1058$
• Weight: $4$
• Character orbit: 1058.e
• Rep. character: $\chi_{1058}(47,\cdot)$
• Character field: $\Q(\zeta_{23})$
• Dimension: $3036$
• Sturm bound: $552$

Defining parameters

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1058.e (of order \(23\) and degree \(22\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 529 \)
Character field:			\(\Q(\zeta_{23})\)
Sturm bound:			\(552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1058, [\chi])\).

	Total	New	Old
Modular forms	9152	3036	6116
Cusp forms	9064	3036	6028
Eisenstein series	88	0	88

Trace form

3036 * q + 8 * q^3 - 552 * q^4 + 194 * q^5 - 84 * q^6 + 84 * q^7 - 1334 * q^9 + 20 * q^10 + 34 * q^11 + 32 * q^12 + 112 * q^13 - 40 * q^14 - 4 * q^15 - 2208 * q^16 - 28 * q^17 + 128 * q^18 - 38 * q^19 + 40 * q^20 + 260 * q^21 + 188 * q^22 - 874 * q^23 + 32 * q^24 - 6690 * q^25 - 192 * q^26 + 404 * q^27 - 32 * q^28 + 164 * q^29 - 480 * q^30 + 68 * q^31 - 2052 * q^33 + 520 * q^34 - 584 * q^35 - 4048 * q^36 - 2226 * q^37 + 436 * q^38 + 444 * q^39 + 80 * q^40 - 452 * q^41 - 3800 * q^42 + 366 * q^43 - 1152 * q^44 + 326 * q^45 + 1564 * q^46 - 1536 * q^47 + 128 * q^48 - 10706 * q^49 + 424 * q^50 + 10648 * q^51 + 448 * q^52 + 6072 * q^53 + 128 * q^54 - 2934 * q^55 - 160 * q^56 - 3564 * q^57 - 296 * q^58 - 6224 * q^59 - 16 * q^60 - 3498 * q^61 + 856 * q^62 - 5572 * q^63 - 8832 * q^64 + 3866 * q^65 - 11312 * q^66 + 13650 * q^67 - 112 * q^68 + 8326 * q^69 - 688 * q^70 + 1816 * q^71 + 512 * q^72 + 524 * q^73 - 220 * q^74 - 3928 * q^75 - 152 * q^76 - 1304 * q^77 - 976 * q^78 - 1948 * q^79 - 2784 * q^80 - 7348 * q^81 + 888 * q^82 - 2146 * q^83 + 1040 * q^84 - 1244 * q^85 - 1380 * q^86 + 17030 * q^87 + 752 * q^88 + 1044 * q^89 - 1176 * q^90 + 1956 * q^91 - 3804 * q^93 - 960 * q^94 - 2468 * q^95 + 128 * q^96 + 428 * q^97 - 832 * q^98 - 12016 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1058, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1058, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1058, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(529, [\chi])\)\(^{\oplus 2}\)