Properties

Label 20.8.a
Level 20
Weight 8
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 20.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(20))\).

Total New Old
Modular forms 24 3 21
Cusp forms 18 3 15
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.
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 125q^{5} \) \(\mathstrut +\mathstrut 954q^{7} \) \(\mathstrut +\mathstrut 2707q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 125q^{5} \) \(\mathstrut +\mathstrut 954q^{7} \) \(\mathstrut +\mathstrut 2707q^{9} \) \(\mathstrut -\mathstrut 240q^{11} \) \(\mathstrut +\mathstrut 9126q^{13} \) \(\mathstrut -\mathstrut 1750q^{15} \) \(\mathstrut +\mathstrut 6318q^{17} \) \(\mathstrut -\mathstrut 19428q^{19} \) \(\mathstrut -\mathstrut 93652q^{21} \) \(\mathstrut +\mathstrut 43518q^{23} \) \(\mathstrut +\mathstrut 46875q^{25} \) \(\mathstrut -\mathstrut 159452q^{27} \) \(\mathstrut +\mathstrut 35562q^{29} \) \(\mathstrut -\mathstrut 261492q^{31} \) \(\mathstrut +\mathstrut 799920q^{33} \) \(\mathstrut +\mathstrut 295750q^{35} \) \(\mathstrut -\mathstrut 191946q^{37} \) \(\mathstrut -\mathstrut 432628q^{39} \) \(\mathstrut -\mathstrut 1042662q^{41} \) \(\mathstrut +\mathstrut 2083230q^{43} \) \(\mathstrut +\mathstrut 876125q^{45} \) \(\mathstrut -\mathstrut 1832862q^{47} \) \(\mathstrut +\mathstrut 137199q^{49} \) \(\mathstrut -\mathstrut 4286724q^{51} \) \(\mathstrut +\mathstrut 3235902q^{53} \) \(\mathstrut +\mathstrut 930000q^{55} \) \(\mathstrut -\mathstrut 1347304q^{57} \) \(\mathstrut -\mathstrut 1362996q^{59} \) \(\mathstrut -\mathstrut 4346634q^{61} \) \(\mathstrut +\mathstrut 7176506q^{63} \) \(\mathstrut +\mathstrut 2154250q^{65} \) \(\mathstrut +\mathstrut 290634q^{67} \) \(\mathstrut -\mathstrut 662844q^{69} \) \(\mathstrut -\mathstrut 805116q^{71} \) \(\mathstrut +\mathstrut 3433686q^{73} \) \(\mathstrut -\mathstrut 406250q^{75} \) \(\mathstrut -\mathstrut 1616880q^{77} \) \(\mathstrut +\mathstrut 5934696q^{79} \) \(\mathstrut -\mathstrut 229433q^{81} \) \(\mathstrut -\mathstrut 5962722q^{83} \) \(\mathstrut +\mathstrut 575250q^{85} \) \(\mathstrut -\mathstrut 3939564q^{87} \) \(\mathstrut -\mathstrut 9031362q^{89} \) \(\mathstrut +\mathstrut 16727892q^{91} \) \(\mathstrut -\mathstrut 26418136q^{93} \) \(\mathstrut -\mathstrut 7689500q^{95} \) \(\mathstrut +\mathstrut 18000534q^{97} \) \(\mathstrut +\mathstrut 746640q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(20))\) 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
20.8.a.a \(1\) \(6.248\) \(\Q\) None \(0\) \(-6\) \(-125\) \(-706\) \(-\) \(+\) \(q-6q^{3}-5^{3}q^{5}-706q^{7}-2151q^{9}+\cdots\)
20.8.a.b \(2\) \(6.248\) \(\Q(\sqrt{1129}) \) None \(0\) \(-20\) \(250\) \(1660\) \(-\) \(-\) \(q+(-10-\beta )q^{3}+5^{3}q^{5}+(830+9\beta )q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)