Properties

Label 4.5.b
Level 4
Weight 5
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{5}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

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