Properties

Label 20.6.a
Level 20
Weight 6
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 20.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(20))\).

Total New Old
Modular forms 18 1 17
Cusp forms 12 1 11
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\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\(q \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut -\mathstrut 25q^{5} \) \(\mathstrut +\mathstrut 218q^{7} \) \(\mathstrut +\mathstrut 241q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut -\mathstrut 25q^{5} \) \(\mathstrut +\mathstrut 218q^{7} \) \(\mathstrut +\mathstrut 241q^{9} \) \(\mathstrut -\mathstrut 480q^{11} \) \(\mathstrut -\mathstrut 622q^{13} \) \(\mathstrut -\mathstrut 550q^{15} \) \(\mathstrut +\mathstrut 186q^{17} \) \(\mathstrut -\mathstrut 1204q^{19} \) \(\mathstrut +\mathstrut 4796q^{21} \) \(\mathstrut -\mathstrut 3186q^{23} \) \(\mathstrut +\mathstrut 625q^{25} \) \(\mathstrut -\mathstrut 44q^{27} \) \(\mathstrut +\mathstrut 5526q^{29} \) \(\mathstrut +\mathstrut 9356q^{31} \) \(\mathstrut -\mathstrut 10560q^{33} \) \(\mathstrut -\mathstrut 5450q^{35} \) \(\mathstrut +\mathstrut 5618q^{37} \) \(\mathstrut -\mathstrut 13684q^{39} \) \(\mathstrut -\mathstrut 14394q^{41} \) \(\mathstrut -\mathstrut 370q^{43} \) \(\mathstrut -\mathstrut 6025q^{45} \) \(\mathstrut +\mathstrut 16146q^{47} \) \(\mathstrut +\mathstrut 30717q^{49} \) \(\mathstrut +\mathstrut 4092q^{51} \) \(\mathstrut -\mathstrut 4374q^{53} \) \(\mathstrut +\mathstrut 12000q^{55} \) \(\mathstrut -\mathstrut 26488q^{57} \) \(\mathstrut -\mathstrut 11748q^{59} \) \(\mathstrut +\mathstrut 13202q^{61} \) \(\mathstrut +\mathstrut 52538q^{63} \) \(\mathstrut +\mathstrut 15550q^{65} \) \(\mathstrut -\mathstrut 11542q^{67} \) \(\mathstrut -\mathstrut 70092q^{69} \) \(\mathstrut -\mathstrut 29532q^{71} \) \(\mathstrut +\mathstrut 33698q^{73} \) \(\mathstrut +\mathstrut 13750q^{75} \) \(\mathstrut -\mathstrut 104640q^{77} \) \(\mathstrut +\mathstrut 31208q^{79} \) \(\mathstrut -\mathstrut 59531q^{81} \) \(\mathstrut -\mathstrut 38466q^{83} \) \(\mathstrut -\mathstrut 4650q^{85} \) \(\mathstrut +\mathstrut 121572q^{87} \) \(\mathstrut +\mathstrut 119514q^{89} \) \(\mathstrut -\mathstrut 135596q^{91} \) \(\mathstrut +\mathstrut 205832q^{93} \) \(\mathstrut +\mathstrut 30100q^{95} \) \(\mathstrut +\mathstrut 94658q^{97} \) \(\mathstrut -\mathstrut 115680q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(20))\) 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
20.6.a.a \(1\) \(3.208\) \(\Q\) None \(0\) \(22\) \(-25\) \(218\) \(-\) \(+\) \(q+22q^{3}-5^{2}q^{5}+218q^{7}+241q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)