Properties

Label 20.5.d
Level 20
Weight 5
Character orbit d
Rep. character \(\chi_{20}(19,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 3
Sturm bound 15
Trace bound 2

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 20 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(15\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(20, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10q - 16q^{4} + 10q^{5} - 16q^{6} + 158q^{9} + O(q^{10}) \) \( 10q - 16q^{4} + 10q^{5} - 16q^{6} + 158q^{9} - 160q^{10} - 16q^{14} - 320q^{16} + 400q^{20} - 632q^{21} + 1664q^{24} - 790q^{25} + 2496q^{26} + 308q^{29} - 2320q^{30} - 2176q^{34} - 8176q^{36} + 6400q^{40} + 2420q^{41} + 1920q^{44} + 2270q^{45} + 14064q^{46} + 638q^{49} - 12480q^{50} - 8992q^{54} - 25216q^{56} + 21120q^{60} - 1580q^{61} + 15104q^{64} - 1920q^{65} + 46080q^{66} - 15992q^{69} - 22800q^{70} - 23616q^{74} - 48000q^{76} + 32320q^{80} - 8302q^{81} + 30208q^{84} + 8960q^{85} + 53744q^{86} + 36308q^{89} - 48480q^{90} - 24336q^{94} - 80896q^{96} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(20, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.5.d.a \(1\) \(2.067\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-4\) \(2\) \(25\) \(82\) \(q-4q^{2}+2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.b \(1\) \(2.067\) \(\Q\) \(\Q(\sqrt{-5}) \) \(4\) \(-2\) \(25\) \(-82\) \(q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.c \(8\) \(2.067\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(-40\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-6+\beta _{3})q^{4}+(-5+\cdots)q^{5}+\cdots\)