Atlas › Modular forms › Weight 6 › Level 107 › 107.6.a

Newspace 107.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(107))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
107.6.a.a	19	degree 19	$19q - 8q^{2} - 35q^{3} + 224q^{4} - 201q^{5} - 87q^{6} - 404q^{7} + O(q^{8})$	+	$-1$
107.6.a.b	25	degree 25	$25q + 4q^{2} + 55q^{3} + 464q^{4} + 149q^{5} + 201q^{6} + 380q^{7} + O(q^{8})$	−	$+1$

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 $T$
107.6.a.a	$x^{19} + 43x^{18} - 2310x^{17} - 101667x^{16} + 2221662x^{15} + 92428092x^{14} - 1244953876x^{13} - 41065545751x^{12} + 464761450750x^{11} + 9333764242895x^{10} - 112672776396412x^{9} - 1005395334566394x^{8} + 15676730195601239x^{7} + 28612674570825566x^{6} - 1069157144017244862x^{5} + 2587972057315470640x^{4} + 24532435833177990592x^{3} - 144978661810715063632x^{2} + 230485485966522794176x - 38430943683093522944$
107.6.a.b	$x^{25} - 59x^{24} - 3456x^{23} + 253294x^{22} + 3910668x^{21} - 439394578x^{20} - 998299544x^{19} + 412473702956x^{18} - 1443467661995x^{17} - 235449846170355x^{16} + 1485342471365875x^{15} + 86431766860733725x^{14} - 655230250411378709x^{13} - 20885274038919762155x^{12} + 165143502115432244665x^{11} + 3318353481847233911713x^{10} - 25165090638779293339161x^{9} - 337703236958638973773121x^{8} + 2291280065261137537822260x^{7} + 20702626239337816415925520x^{6} - 116209500871394322636424684x^{5} - 674740192221856454077542620x^{4} + 2728605558791848301144165200x^{3} + 8988208753262057014903547488x^{2} - 14392492587796328071214353504x - 31643015214665313867411339904$

Orbit

Characteristic polynomial of

T

107.6.a.a

x^{19} + 43x^{18} - 2310x^{17} - 101667x^{16} + 2221662x^{15} + 92428092x^{14} - 1244953876x^{13} - 41065545751x^{12} + 464761450750x^{11} + 9333764242895x^{10} - 112672776396412x^{9} - 1005395334566394x^{8} + 15676730195601239x^{7} + 28612674570825566x^{6} - 1069157144017244862x^{5} + 2587972057315470640x^{4} + 24532435833177990592x^{3} - 144978661810715063632x^{2} + 230485485966522794176x - 38430943683093522944

107.6.a.b

x^{25} - 59x^{24} - 3456x^{23} + 253294x^{22} + 3910668x^{21} - 439394578x^{20} - 998299544x^{19} + 412473702956x^{18} - 1443467661995x^{17} - 235449846170355x^{16} + 1485342471365875x^{15} + 86431766860733725x^{14} - 655230250411378709x^{13} - 20885274038919762155x^{12} + 165143502115432244665x^{11} + 3318353481847233911713x^{10} - 25165090638779293339161x^{9} - 337703236958638973773121x^{8} + 2291280065261137537822260x^{7} + 20702626239337816415925520x^{6} - 116209500871394322636424684x^{5} - 674740192221856454077542620x^{4} + 2728605558791848301144165200x^{3} + 8988208753262057014903547488x^{2} - 14392492587796328071214353504x - 31643015214665313867411339904

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(107))$	44
Old forms	0
Cusp forms $S_{6}(\Gamma_0(107))$	44
Eisenstein series $E_{6}(\Gamma_0(107))$	2
Modular forms $M_{6}(\Gamma_0(107))$	46

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.277 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, 107]: [1, 46] (certified at ell = 2147482621)
T = [(2, 1), (3, 1)]; h of degree 44 = 1 x 44 (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(107, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 107:6 1000

← 106.6.a · 108.6.a →