Atlas › Modular forms › Weight 6 › Level 103 › 103.6.a

Newspace 103.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(103))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
103.6.a.a	19	degree 19	$19q - 21q^{2} - 38q^{3} + 271q^{4} - 147q^{5} - 137q^{6} - 206q^{7} + O(q^{8})$	+	$-1$
103.6.a.b	24	degree 24	$24q + 19q^{2} + 16q^{3} + 431q^{4} + 153q^{5} + 79q^{6} + 186q^{7} + O(q^{8})$	−	$+1$

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 $T$
103.6.a.a	$x^{19} + 59x^{18} - 1259x^{17} - 115634x^{16} + 297028x^{15} + 87916042x^{14} + 111694134x^{13} - 34453824454x^{12} - 32107600436x^{11} + 7632468898320x^{10} - 7400851566048x^{9} - 946362610021818x^{8} + 3132607904056225x^{7} + 58403721711916643x^{6} - 344036949173262441x^{5} - 1071586133148306950x^{4} + 12434520790741172708x^{3} - 26114786961301924872x^{2} - 8120478403539106960x + 46404360183877805248$
103.6.a.b	$x^{24} - 35x^{23} - 4383x^{22} + 148980x^{21} + 8311278x^{20} - 267518025x^{19} - 9078671965x^{18} + 266355207017x^{17} + 6399371770322x^{16} - 162162357188462x^{15} - 3075492210238726x^{14} + 62635875528303158x^{13} + 1030175978246886509x^{12} - 15337392073989523707x^{11} - 239317938640135857571x^{10} + 2277313446476760809086x^{9} + 37302206430043010007360x^{8} - 177309460718736986968869x^{7} - 3630455695043346187527617x^{6} + 3104017908306489069798077x^{5} + 189704115896341021105174872x^{4} + 413534408898629635603783436x^{3} - 3455787368767587163837300080x^{2} - 16587599604975377746852804080x - 19605100753764986764003901280$

Orbit

Characteristic polynomial of

T

103.6.a.a

x^{19} + 59x^{18} - 1259x^{17} - 115634x^{16} + 297028x^{15} + 87916042x^{14} + 111694134x^{13} - 34453824454x^{12} - 32107600436x^{11} + 7632468898320x^{10} - 7400851566048x^{9} - 946362610021818x^{8} + 3132607904056225x^{7} + 58403721711916643x^{6} - 344036949173262441x^{5} - 1071586133148306950x^{4} + 12434520790741172708x^{3} - 26114786961301924872x^{2} - 8120478403539106960x + 46404360183877805248

103.6.a.b

x^{24} - 35x^{23} - 4383x^{22} + 148980x^{21} + 8311278x^{20} - 267518025x^{19} - 9078671965x^{18} + 266355207017x^{17} + 6399371770322x^{16} - 162162357188462x^{15} - 3075492210238726x^{14} + 62635875528303158x^{13} + 1030175978246886509x^{12} - 15337392073989523707x^{11} - 239317938640135857571x^{10} + 2277313446476760809086x^{9} + 37302206430043010007360x^{8} - 177309460718736986968869x^{7} - 3630455695043346187527617x^{6} + 3104017908306489069798077x^{5} + 189704115896341021105174872x^{4} + 413534408898629635603783436x^{3} - 3455787368767587163837300080x^{2} - 16587599604975377746852804080x - 19605100753764986764003901280

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(103))$	43
Old forms	0
Cusp forms $S_{6}(\Gamma_0(103))$	43
Eisenstein series $E_{6}(\Gamma_0(103))$	2
Modular forms $M_{6}(\Gamma_0(103))$	45

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.273 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, 103]: [1, 45] (certified at ell = 2147482501)
T = [(2, 1), (3, 1)]; h of degree 43 = 1 x 43 (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(103, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 103:6 1000

← 102.6.a · 104.6.a →