Atlas › Modular forms › Weight 6 › Level 101 › 101.6.a

Newspace 101.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(101))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
101.6.a.a	17	degree 17	$17q - 5q^{2} - 46q^{3} + 143q^{4} - 79q^{5} - 194q^{6} - 198q^{7} + O(q^{8})$	+	$-1$
101.6.a.b	24	degree 24	$24q + 7q^{2} + 44q^{3} + 479q^{4} + 21q^{5} + 22q^{6} + 390q^{7} + O(q^{8})$	−	$+1$

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 $T$
101.6.a.a	$x^{17} + 51x^{16} - 1333x^{15} - 90939x^{14} + 550059x^{13} + 61816357x^{12} - 91966089x^{11} - 20606819783x^{10} + 23465027639x^{9} + 3487669621405x^{8} - 8222153409293x^{7} - 263261707513947x^{6} + 975087544280059x^{5} + 6373616069106241x^{4} - 31146672210033994x^{3} - 9314680464241778x^{2} + 175803399082912552x - 168122683175015208$
101.6.a.b	$x^{24} - 51x^{23} - 3530x^{22} + 201726x^{21} + 5046920x^{20} - 335145650x^{19} - 3896928639x^{18} + 309878762341x^{17} + 1904326733059x^{16} - 178197998113737x^{15} - 702428934652193x^{14} + 67070469509876795x^{13} + 230682716329425697x^{12} - 16771081577643325261x^{11} - 65685029738146957430x^{10} + 2735016961389269047202x^{9} + 13622388853429951480167x^{8} - 272564043296847623233655x^{7} - 1760938505600754822379967x^{6} + 14053694791704046900902685x^{5} + 121410130611924085795427892x^{4} - 194782992383171263760754386x^{3} - 3269265409770992893681401888x^{2} - 4858033344535080234112603832x + 6923908099239411794747316768$

Orbit

Characteristic polynomial of

T

101.6.a.a

x^{17} + 51x^{16} - 1333x^{15} - 90939x^{14} + 550059x^{13} + 61816357x^{12} - 91966089x^{11} - 20606819783x^{10} + 23465027639x^{9} + 3487669621405x^{8} - 8222153409293x^{7} - 263261707513947x^{6} + 975087544280059x^{5} + 6373616069106241x^{4} - 31146672210033994x^{3} - 9314680464241778x^{2} + 175803399082912552x - 168122683175015208

101.6.a.b

x^{24} - 51x^{23} - 3530x^{22} + 201726x^{21} + 5046920x^{20} - 335145650x^{19} - 3896928639x^{18} + 309878762341x^{17} + 1904326733059x^{16} - 178197998113737x^{15} - 702428934652193x^{14} + 67070469509876795x^{13} + 230682716329425697x^{12} - 16771081577643325261x^{11} - 65685029738146957430x^{10} + 2735016961389269047202x^{9} + 13622388853429951480167x^{8} - 272564043296847623233655x^{7} - 1760938505600754822379967x^{6} + 14053694791704046900902685x^{5} + 121410130611924085795427892x^{4} - 194782992383171263760754386x^{3} - 3269265409770992893681401888x^{2} - 4858033344535080234112603832x + 6923908099239411794747316768

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(101))$	41
Old forms	0
Cusp forms $S_{6}(\Gamma_0(101))$	41
Eisenstein series $E_{6}(\Gamma_0(101))$	2
Modular forms $M_{6}(\Gamma_0(101))$	43

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.264 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, 101]: [1, 43] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 41 = 1 x 41 (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(101, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 101:6 1000

← 100.6.a · 102.6.a →