Properties

Label 16.4.a
Level 16
Weight 4
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 8
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(16))\).

Total New Old
Modular forms 9 2 7
Cusp forms 3 1 2
Eisenstein series 6 1 5

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 \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.4.a.a \(1\) \(0.944\) \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) \(+\) \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)

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