Properties

Label 8.4.a
Level 8
Weight 4
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 4
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(8))\).

Total New Old
Modular forms 5 1 4
Cusp forms 1 1 0
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(+\)\(1\)

Trace form

\( q - 4q^{3} - 2q^{5} + 24q^{7} - 11q^{9} + O(q^{10}) \) \( q - 4q^{3} - 2q^{5} + 24q^{7} - 11q^{9} - 44q^{11} + 22q^{13} + 8q^{15} + 50q^{17} + 44q^{19} - 96q^{21} - 56q^{23} - 121q^{25} + 152q^{27} + 198q^{29} - 160q^{31} + 176q^{33} - 48q^{35} - 162q^{37} - 88q^{39} - 198q^{41} + 52q^{43} + 22q^{45} + 528q^{47} + 233q^{49} - 200q^{51} - 242q^{53} + 88q^{55} - 176q^{57} - 668q^{59} + 550q^{61} - 264q^{63} - 44q^{65} + 188q^{67} + 224q^{69} + 728q^{71} + 154q^{73} + 484q^{75} - 1056q^{77} - 656q^{79} - 311q^{81} + 236q^{83} - 100q^{85} - 792q^{87} + 714q^{89} + 528q^{91} + 640q^{93} - 88q^{95} - 478q^{97} + 484q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
8.4.a.a \(1\) \(0.472\) \(\Q\) None \(0\) \(-4\) \(-2\) \(24\) \(+\) \(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 4 T + 27 T^{2} \)
$5$ \( 1 + 2 T + 125 T^{2} \)
$7$ \( 1 - 24 T + 343 T^{2} \)
$11$ \( 1 + 44 T + 1331 T^{2} \)
$13$ \( 1 - 22 T + 2197 T^{2} \)
$17$ \( 1 - 50 T + 4913 T^{2} \)
$19$ \( 1 - 44 T + 6859 T^{2} \)
$23$ \( 1 + 56 T + 12167 T^{2} \)
$29$ \( 1 - 198 T + 24389 T^{2} \)
$31$ \( 1 + 160 T + 29791 T^{2} \)
$37$ \( 1 + 162 T + 50653 T^{2} \)
$41$ \( 1 + 198 T + 68921 T^{2} \)
$43$ \( 1 - 52 T + 79507 T^{2} \)
$47$ \( 1 - 528 T + 103823 T^{2} \)
$53$ \( 1 + 242 T + 148877 T^{2} \)
$59$ \( 1 + 668 T + 205379 T^{2} \)
$61$ \( 1 - 550 T + 226981 T^{2} \)
$67$ \( 1 - 188 T + 300763 T^{2} \)
$71$ \( 1 - 728 T + 357911 T^{2} \)
$73$ \( 1 - 154 T + 389017 T^{2} \)
$79$ \( 1 + 656 T + 493039 T^{2} \)
$83$ \( 1 - 236 T + 571787 T^{2} \)
$89$ \( 1 - 714 T + 704969 T^{2} \)
$97$ \( 1 + 478 T + 912673 T^{2} \)
show more
show less