Atlas › Modular forms › Weight 2 › Level 877 › 877.2.a

Newspace 877.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(877))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
877.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - 2q^{3} + 6q^{4} - 2q^{5} - 10q^{6} + O(q^{8})$	+	$-1$
877.2.a.b	32	degree 32	$32q - 9q^{2} - 20q^{3} + 25q^{4} - 19q^{5} + 3q^{6} - 17q^{7} + O(q^{8})$	+	$-1$
877.2.a.c	38	degree 38	$38q + 7q^{2} + 22q^{3} + 39q^{4} + 21q^{5} + 7q^{6} + 15q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
877.2.a.a	$x^{2} + 6x - 11$
877.2.a.b	$x^{32} + 69x^{31} + 1778x^{30} + 15549x^{29} - 168426x^{28} - 4695025x^{27} - 22483660x^{26} + 321128808x^{25} + 4023231802x^{24} - 370038111x^{23} - 234499880248x^{22} - 914194456414x^{21} + 6308177209263x^{20} + 48925343044830x^{19} - 57041665175976x^{18} - 1269326895735559x^{17} - 1085930380057458x^{16} + 19209179682916951x^{15} + 36998562952447491x^{14} - 181043131826930010x^{13} - 460857463971473688x^{12} + 1126197392760259510x^{11} + 3038270159686244984x^{10} - 4989272508666355713x^{9} - 10583344338027600658x^{8} + 16021349428423346191x^{7} + 14776425462538168368x^{6} - 29234617148247930805x^{5} + 5136218994186844022x^{4} + 8866361561418472324x^{3} - 3306847657097582439x^{2} - 499830006129990832x + 251207100080882609$
877.2.a.c	$x^{38} - 73x^{37} + 1875x^{36} - 9536x^{35} - 468577x^{34} + 8847973x^{33} - 4195877x^{32} - 1399884399x^{31} + 11606807742x^{30} + 78415041539x^{29} - 1569052910306x^{28} + 1775212778014x^{27} + 101619329508711x^{26} - 521475934960091x^{25} - 3437496463626383x^{24} + 34945736631799296x^{23} + 35107052972407973x^{22} - 1301316953863533142x^{21} + 1974646563280128210x^{20} + 30014080540214388732x^{19} - 100908266591519162575x^{18} - 423402033876336094356x^{17} + 2335254793458096959145x^{16} + 3114600735840473510080x^{15} - 32397525502881499747157x^{14} - 480809322727526630310x^{13} + 282051802068638894609672x^{12} - 197329935105270671682691x^{11} - 1520118253701132103915608x^{10} + 1628003796915493201473997x^{9} + 4811194799192841134424975x^{8} - 5699900713271527141910182x^{7} - 7915506754295583024331230x^{6} + 8741025444603962198248333x^{5} + 4766260220936457385284088x^{4} - 5333841745602798912139034x^{3} - 572360126776219505075320x^{2} + 1091007111842176906373286x - 181869867446789552723027$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(877))$	72
Old forms	0
Cusp forms $S_{2}(\Gamma_0(877))$	72
Eisenstein series $E_{2}(\Gamma_0(877))$	1
Modular forms $M_{2}(\Gamma_0(877))$	73

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.295 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

dim M^+ at levels [1, 877]: [0, 73] (certified at ell = 2147478961)
T = [(2, 1), (3, 3)]; h of degree 72 = 1 x 72 (phi(ord eps) x dim S_k^new); 10 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(877, 2)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 877:2 1000

← 876.2.a · 878.2.a →