Space of modular forms of level 529, weight 4, and Character 529.g

• Label: 529.4.g
• Level: $529$
• Weight: $4$
• Character orbit: 529.g
• Rep. character: $\chi_{529}(2,\cdot)$
• Character field: $\Q(\zeta_{253})$
• Dimension: $30140$
• Sturm bound: $184$

Defining parameters

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.g (of order \(253\) and degree \(220\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 529 \)
Character field:			\(\Q(\zeta_{253})\)
Sturm bound:			\(184\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(529, [\chi])\).

	Total	New	Old
Modular forms	30580	30580	0
Cusp forms	30140	30140	0
Eisenstein series	440	440	0

Trace form

30140 * q - 219 * q^2 - 217 * q^3 + 325 * q^4 - 119 * q^5 - 333 * q^6 - 165 * q^7 - 255 * q^8 + 934 * q^9 - 277 * q^10 + 53 * q^11 - 227 * q^12 - 165 * q^13 - 347 * q^14 + 195 * q^15 + 2381 * q^16 - 113 * q^17 - 161 * q^18 - 579 * q^19 - 759 * q^20 - 659 * q^21 + 817 * q^22 - 1646 * q^23 - 636 * q^24 + 1168 * q^25 - 389 * q^26 - 361 * q^27 - 2106 * q^28 + 211 * q^29 + 811 * q^30 + 197 * q^31 + 709 * q^32 - 391 * q^33 + 6523 * q^34 + 487 * q^35 + 10506 * q^36 - 1091 * q^37 + 1274 * q^38 - 207 * q^39 - 1709 * q^40 - 783 * q^41 - 7130 * q^42 - 1845 * q^43 - 6612 * q^44 - 2998 * q^45 - 2615 * q^46 - 1414 * q^47 - 2257 * q^48 + 2316 * q^49 - 400 * q^50 + 4011 * q^51 + 1467 * q^52 + 3013 * q^53 + 5227 * q^54 + 8445 * q^55 + 6982 * q^56 - 7235 * q^57 + 3456 * q^58 + 181 * q^59 + 2927 * q^60 - 13799 * q^61 - 3892 * q^62 - 20428 * q^63 + 3513 * q^64 + 1959 * q^65 - 16844 * q^66 + 6781 * q^67 - 8580 * q^68 + 4367 * q^69 + 7078 * q^70 - 3383 * q^71 - 5034 * q^72 - 1121 * q^73 - 20166 * q^74 - 179 * q^75 + 3368 * q^76 + 5157 * q^77 + 392 * q^78 + 2329 * q^79 - 898 * q^80 + 23496 * q^81 + 5847 * q^82 + 3737 * q^83 + 9002 * q^84 - 417 * q^85 - 951 * q^86 + 7159 * q^87 - 6055 * q^88 - 3947 * q^89 - 22952 * q^90 - 7468 * q^91 + 409 * q^92 - 2300 * q^93 - 5542 * q^94 - 4489 * q^95 - 2888 * q^96 + 2189 * q^97 + 4099 * q^98 - 11435 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(529, [\chi])\) into newform subspaces

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