Atlas › Modular forms › Weight 2 › Level 967 › 967.2.a

Newspace 967.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(967))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
967.2.a.a	35	degree 35	$35q - 12q^{2} - 11q^{3} + 32q^{4} - 27q^{5} - 6q^{6} - 12q^{7} + O(q^{8})$	+	$-1$
967.2.a.b	45	degree 45	$45q + 11q^{2} + 11q^{3} + 47q^{4} + 27q^{5} + 4q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
967.2.a.a	$x^{35} + 23x^{34} + 157x^{33} - 275x^{32} - 7931x^{31} - 21604x^{30} + 125751x^{29} + 715221x^{28} - 540993x^{27} - 10055055x^{26} - 8084194x^{25} + 81121124x^{24} + 142259923x^{23} - 406849256x^{22} - 1085585938x^{21} + 1265676935x^{20} + 5110662291x^{19} - 2144821487x^{18} - 16250296278x^{17} + 334126191x^{16} + 36172644813x^{15} + 7345112212x^{14} - 57131568928x^{13} - 18104326038x^{12} + 63947323549x^{11} + 22429004747x^{10} - 49896548154x^{9} - 16072876325x^{8} + 26103177304x^{7} + 6465397725x^{6} - 8448205162x^{5} - 1266298976x^{4} + 1418270490x^{3} + 90855099x^{2} - 73124168x - 7701533$
967.2.a.b	$x^{45} - 22x^{44} + 75x^{43} + 1750x^{42} - 14781x^{41} - 36713x^{40} + 777960x^{39} - 909371x^{38} - 20729174x^{37} + 66512095x^{36} + 308026081x^{35} - 1688941388x^{34} - 2202719072x^{33} + 24963132633x^{32} - 4430649564x^{31} - 238612202786x^{30} + 261470953889x^{29} + 1522140319437x^{28} - 2787045246124x^{27} - 6468617866370x^{26} + 16893390290002x^{25} + 17704002412342x^{24} - 66697994368742x^{23} - 28040636861569x^{22} + 179013239396914x^{21} + 14464858690701x^{20} - 331133562900364x^{19} + 32024124900740x^{18} + 420836492835677x^{17} - 71215891538934x^{16} - 360449807769639x^{15} + 61485701110546x^{14} + 200227218191068x^{13} - 25520835560203x^{12} - 67683897147843x^{11} + 4435064638067x^{10} + 12503892827110x^{9} - 223907061784x^{8} - 1038272531821x^{7} + 38637285331x^{6} + 35133870202x^{5} - 3204299072x^{4} - 195873060x^{3} + 28999222x^{2} - 677913x - 3717$

Orbit

Characteristic polynomial of

T

967.2.a.a

x^{35} + 23x^{34} + 157x^{33} - 275x^{32} - 7931x^{31} - 21604x^{30} + 125751x^{29} + 715221x^{28} - 540993x^{27} - 10055055x^{26} - 8084194x^{25} + 81121124x^{24} + 142259923x^{23} - 406849256x^{22} - 1085585938x^{21} + 1265676935x^{20} + 5110662291x^{19} - 2144821487x^{18} - 16250296278x^{17} + 334126191x^{16} + 36172644813x^{15} + 7345112212x^{14} - 57131568928x^{13} - 18104326038x^{12} + 63947323549x^{11} + 22429004747x^{10} - 49896548154x^{9} - 16072876325x^{8} + 26103177304x^{7} + 6465397725x^{6} - 8448205162x^{5} - 1266298976x^{4} + 1418270490x^{3} + 90855099x^{2} - 73124168x - 7701533

967.2.a.b

x^{45} - 22x^{44} + 75x^{43} + 1750x^{42} - 14781x^{41} - 36713x^{40} + 777960x^{39} - 909371x^{38} - 20729174x^{37} + 66512095x^{36} + 308026081x^{35} - 1688941388x^{34} - 2202719072x^{33} + 24963132633x^{32} - 4430649564x^{31} - 238612202786x^{30} + 261470953889x^{29} + 1522140319437x^{28} - 2787045246124x^{27} - 6468617866370x^{26} + 16893390290002x^{25} + 17704002412342x^{24} - 66697994368742x^{23} - 28040636861569x^{22} + 179013239396914x^{21} + 14464858690701x^{20} - 331133562900364x^{19} + 32024124900740x^{18} + 420836492835677x^{17} - 71215891538934x^{16} - 360449807769639x^{15} + 61485701110546x^{14} + 200227218191068x^{13} - 25520835560203x^{12} - 67683897147843x^{11} + 4435064638067x^{10} + 12503892827110x^{9} - 223907061784x^{8} - 1038272531821x^{7} + 38637285331x^{6} + 35133870202x^{5} - 3204299072x^{4} - 195873060x^{3} + 28999222x^{2} - 677913x - 3717

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(967))$	80
Old forms	0
Cusp forms $S_{2}(\Gamma_0(967))$	80
Eisenstein series $E_{2}(\Gamma_0(967))$	1
Modular forms $M_{2}(\Gamma_0(967))$	81

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.305 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, 967]: [0, 81] (certified at ell = 2147480791)
T = [(2, 1), (3, 1)]; h of degree 80 = 1 x 80 (phi(ord eps) x dim S_k^new); 8 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(967, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 967:2 1000

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