Properties

Label 4.5.b
Level 4
Weight 5
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 2
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(4, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 4q^{2} + 16q^{4} - 14q^{5} - 64q^{8} + 81q^{9} + O(q^{10}) \) \( q - 4q^{2} + 16q^{4} - 14q^{5} - 64q^{8} + 81q^{9} + 56q^{10} - 238q^{13} + 256q^{16} + 322q^{17} - 324q^{18} - 224q^{20} - 429q^{25} + 952q^{26} + 82q^{29} - 1024q^{32} - 1288q^{34} + 1296q^{36} + 2162q^{37} + 896q^{40} - 3038q^{41} - 1134q^{45} + 2401q^{49} + 1716q^{50} - 3808q^{52} + 2482q^{53} - 328q^{58} - 6958q^{61} + 4096q^{64} + 3332q^{65} + 5152q^{68} - 5184q^{72} + 1442q^{73} - 8648q^{74} - 3584q^{80} + 6561q^{81} + 12152q^{82} - 4508q^{85} - 9758q^{89} + 4536q^{90} - 1918q^{97} - 9604q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.5.b.a \(1\) \(0.413\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(-14\) \(0\) \(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T \)
$3$ \( ( 1 - 9 T )( 1 + 9 T ) \)
$5$ \( 1 + 14 T + 625 T^{2} \)
$7$ \( ( 1 - 49 T )( 1 + 49 T ) \)
$11$ \( ( 1 - 121 T )( 1 + 121 T ) \)
$13$ \( 1 + 238 T + 28561 T^{2} \)
$17$ \( 1 - 322 T + 83521 T^{2} \)
$19$ \( ( 1 - 361 T )( 1 + 361 T ) \)
$23$ \( ( 1 - 529 T )( 1 + 529 T ) \)
$29$ \( 1 - 82 T + 707281 T^{2} \)
$31$ \( ( 1 - 961 T )( 1 + 961 T ) \)
$37$ \( 1 - 2162 T + 1874161 T^{2} \)
$41$ \( 1 + 3038 T + 2825761 T^{2} \)
$43$ \( ( 1 - 1849 T )( 1 + 1849 T ) \)
$47$ \( ( 1 - 2209 T )( 1 + 2209 T ) \)
$53$ \( 1 - 2482 T + 7890481 T^{2} \)
$59$ \( ( 1 - 3481 T )( 1 + 3481 T ) \)
$61$ \( 1 + 6958 T + 13845841 T^{2} \)
$67$ \( ( 1 - 4489 T )( 1 + 4489 T ) \)
$71$ \( ( 1 - 5041 T )( 1 + 5041 T ) \)
$73$ \( 1 - 1442 T + 28398241 T^{2} \)
$79$ \( ( 1 - 6241 T )( 1 + 6241 T ) \)
$83$ \( ( 1 - 6889 T )( 1 + 6889 T ) \)
$89$ \( 1 + 9758 T + 62742241 T^{2} \)
$97$ \( 1 + 1918 T + 88529281 T^{2} \)
show more
show less