Atlas

Modular forms

Every Galois orbit of newforms of weight 2 and level $N \le 1000$ , and of weight 4 to 12 with $Nk^2 \le 4000$ (trivial character): 7,961 orbits in 1,490 spaces, computed and proven by Sagebrush's Rust engines, with LMFDB's labels. The 5,951 weight-2 orbits agree with the LMFDB, every one: label, dimension and $\operatorname{tr} a_p$ for every $p < 1000$ . A space that is not stored is computed in your browser, by the same engine compiled to WebAssembly, and any stored page can be recomputed there to check it.

Examples

11.2.a.a · The first newform
Level 11, attached to the elliptic curve 11a1: q − 2q² − q³ + 2q⁴ + …37.2.a.a · Rank one
The first elliptic curve of positive rank: sign −1.389.2.a.a · Rank two
The smallest conductor of a curve of rank 2.389.2.a.e · Dimension 20
The big orbit at level 389: a degree-20 coefficient field.23.2.a.a · The golden field
Coefficients in ℚ(√5): the first orbit of dimension 2.27.2.a.a · Complex multiplication
CM by ℚ(√−3): a_p = 0 at every inert prime.1.12.a.a · Ramanujan's Δ
q∏(1 − qⁿ)²⁴ = q − 24q² + 252q³ − …1.24.a · Weight 24, live
Not stored: your browser computes it in seconds. Two conjugate newforms with coefficients in ℚ(√144169), as Maeda's conjecture predicts.

Browse newform orbits by weight and level

Weight	1–50	51–100	101–200	201–300	301–400	401–500	501–600	601–700	701–800	801–900	901–1000
2	40	103	327	452	548	612	688	713	784	825	859
4	104	207	552	315
6	141	233	49
8	164	47
10	120
12	78

Search

Compute a space

Any level and even weight with the trivial character: stored spaces open at once; others are computed on the page, after the engine predicts how long that takes (about a second at level 1000, seconds to a minute in the thousands).

For agents

Every page is also JSON: append .json (/atlas/mf/389.2.a.e.json), or search with format=json. The data is static files: stats.json, index.json (one row per orbit) and /atlas/data/mf/k/N.json (a whole newspace, traces $a_1, \dots, a_{1000}$ ). llms.txt describes the formats; in a browser with WebMCP, this page offers the tools atlas_lookup, atlas_search, atlas_estimate and atlas_compute. The largest stored orbit has dimension 55.

Weight	1–50	51–100	101–200	201–300	301–400	401–500	501–600	601–700	701–800	801–900	901–1000
2	40	103	327	452	548	612	688	713	784	825	859
4	104	207	552	315
6	141	233	49
8	164	47
10	120
12	78

Weight	1–50	51–100	101–200	201–300	301–400	401–500	501–600	601–700	701–800	801–900	901–1000
2	40	103	327	452	548	612	688	713	784	825	859
4	104	207	552	315
6	141	233	49
8	164	47
10	120
12	78

Weight	1–50	51–100	101–200	201–300	301–400	401–500	501–600	601–700	701–800	801–900	901–1000
2	40	103	327	452	548	612	688	713	784	825	859
4	104	207	552	315
6	141	233	49
8	164	47
10	120
12	78