Atlas › Modular forms › Weight 4 › Level 223 › 223.4.a

Newspace 223.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(223))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
223.4.a.a	24	degree 24	$24q - 17q^{2} - 8q^{3} + 79q^{4} - 50q^{5} - 14q^{6} - 61q^{7} + O(q^{8})$	−	$-1$
223.4.a.b	31	degree 31	$31q + 15q^{2} + 10q^{3} + 135q^{4} + 50q^{5} + 46q^{6} + 51q^{7} + O(q^{8})$	+	$+1$

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 $T$
223.4.a.a	$x^{24} + 25x^{23} - 166x^{22} - 7851x^{21} - 1695x^{20} + 1056578x^{19} + 2114042x^{18} - 80522809x^{17} - 184356777x^{16} + 3864419084x^{15} + 7016026540x^{14} - 121917165119x^{13} - 113929446191x^{12} + 2522800981400x^{11} - 188337143952x^{10} - 32539471931265x^{9} + 34337034410670x^{8} + 229592398119321x^{7} - 471809749664904x^{6} - 569568643687732x^{5} + 2293408602086880x^{4} - 1219531034801600x^{3} - 1755117314824448x^{2} + 1632270456201216x - 6729628368896$
223.4.a.b	$x^{31} - 25x^{30} - 534x^{29} + 17139x^{28} + 95137x^{27} - 4935216x^{26} - 3288668x^{25} + 799976620x^{24} - 1180760182x^{23} - 82282799516x^{22} + 204437421503x^{21} + 5714064354746x^{20} - 16440889274317x^{19} - 277021835160278x^{18} + 796530753294439x^{17} + 9518573462720808x^{16} - 24804071174949744x^{15} - 231886084788760231x^{14} + 502370182660311413x^{13} + 3949959875116006735x^{12} - 6485432426242617738x^{11} - 45658063344273582254x^{10} + 50345939822631790831x^{9} + 340138341453365245992x^{8} - 204479294589134954925x^{7} - 1496252500729924077584x^{6} + 260091821726843081248x^{5} + 3302326020111355102600x^{4} + 490865589689854667792x^{3} - 2524151216195599868640x^{2} - 869928183437712630912x + 189423682021911177216$

Orbit

Characteristic polynomial of

T

223.4.a.a

x^{24} + 25x^{23} - 166x^{22} - 7851x^{21} - 1695x^{20} + 1056578x^{19} + 2114042x^{18} - 80522809x^{17} - 184356777x^{16} + 3864419084x^{15} + 7016026540x^{14} - 121917165119x^{13} - 113929446191x^{12} + 2522800981400x^{11} - 188337143952x^{10} - 32539471931265x^{9} + 34337034410670x^{8} + 229592398119321x^{7} - 471809749664904x^{6} - 569568643687732x^{5} + 2293408602086880x^{4} - 1219531034801600x^{3} - 1755117314824448x^{2} + 1632270456201216x - 6729628368896

223.4.a.b

x^{31} - 25x^{30} - 534x^{29} + 17139x^{28} + 95137x^{27} - 4935216x^{26} - 3288668x^{25} + 799976620x^{24} - 1180760182x^{23} - 82282799516x^{22} + 204437421503x^{21} + 5714064354746x^{20} - 16440889274317x^{19} - 277021835160278x^{18} + 796530753294439x^{17} + 9518573462720808x^{16} - 24804071174949744x^{15} - 231886084788760231x^{14} + 502370182660311413x^{13} + 3949959875116006735x^{12} - 6485432426242617738x^{11} - 45658063344273582254x^{10} + 50345939822631790831x^{9} + 340138341453365245992x^{8} - 204479294589134954925x^{7} - 1496252500729924077584x^{6} + 260091821726843081248x^{5} + 3302326020111355102600x^{4} + 490865589689854667792x^{3} - 2524151216195599868640x^{2} - 869928183437712630912x + 189423682021911177216

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(223))$	55
Old forms	0
Cusp forms $S_{4}(\Gamma_0(223))$	55
Eisenstein series $E_{4}(\Gamma_0(223))$	2
Modular forms $M_{4}(\Gamma_0(223))$	57

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.151 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, 223]: [1, 57] (certified at ell = 2147482591)
T = [(2, 1), (3, 1)]; h of degree 55 = 1 x 55 (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(223, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 223:4 1000

← 222.4.a · 224.4.a →