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

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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

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

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

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