Properties

Label 20.4.a
Level 20
Weight 4
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(20))\).

Total New Old
Modular forms 12 1 11
Cusp forms 6 1 5
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut -\mathstrut 60q^{11} \) \(\mathstrut +\mathstrut 86q^{13} \) \(\mathstrut +\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut -\mathstrut 64q^{21} \) \(\mathstrut +\mathstrut 48q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 152q^{27} \) \(\mathstrut -\mathstrut 186q^{29} \) \(\mathstrut +\mathstrut 176q^{31} \) \(\mathstrut -\mathstrut 240q^{33} \) \(\mathstrut -\mathstrut 80q^{35} \) \(\mathstrut +\mathstrut 254q^{37} \) \(\mathstrut +\mathstrut 344q^{39} \) \(\mathstrut +\mathstrut 186q^{41} \) \(\mathstrut -\mathstrut 100q^{43} \) \(\mathstrut -\mathstrut 55q^{45} \) \(\mathstrut +\mathstrut 168q^{47} \) \(\mathstrut -\mathstrut 87q^{49} \) \(\mathstrut +\mathstrut 72q^{51} \) \(\mathstrut -\mathstrut 498q^{53} \) \(\mathstrut -\mathstrut 300q^{55} \) \(\mathstrut +\mathstrut 176q^{57} \) \(\mathstrut -\mathstrut 252q^{59} \) \(\mathstrut -\mathstrut 58q^{61} \) \(\mathstrut +\mathstrut 176q^{63} \) \(\mathstrut +\mathstrut 430q^{65} \) \(\mathstrut -\mathstrut 1036q^{67} \) \(\mathstrut +\mathstrut 192q^{69} \) \(\mathstrut +\mathstrut 168q^{71} \) \(\mathstrut +\mathstrut 506q^{73} \) \(\mathstrut +\mathstrut 100q^{75} \) \(\mathstrut +\mathstrut 960q^{77} \) \(\mathstrut +\mathstrut 272q^{79} \) \(\mathstrut -\mathstrut 311q^{81} \) \(\mathstrut +\mathstrut 948q^{83} \) \(\mathstrut +\mathstrut 90q^{85} \) \(\mathstrut -\mathstrut 744q^{87} \) \(\mathstrut -\mathstrut 1014q^{89} \) \(\mathstrut -\mathstrut 1376q^{91} \) \(\mathstrut +\mathstrut 704q^{93} \) \(\mathstrut +\mathstrut 220q^{95} \) \(\mathstrut -\mathstrut 766q^{97} \) \(\mathstrut +\mathstrut 660q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(20))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
20.4.a.a \(1\) \(1.180\) \(\Q\) None \(0\) \(4\) \(5\) \(-16\) \(-\) \(-\) \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)