Properties

Label 20.10.a
Level 20
Weight 10
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 30
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 20.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(20))\).

Total New Old
Modular forms 30 3 27
Cusp forms 24 3 21
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.
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 308q^{3} \) \(\mathstrut -\mathstrut 625q^{5} \) \(\mathstrut -\mathstrut 912q^{7} \) \(\mathstrut +\mathstrut 17503q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 308q^{3} \) \(\mathstrut -\mathstrut 625q^{5} \) \(\mathstrut -\mathstrut 912q^{7} \) \(\mathstrut +\mathstrut 17503q^{9} \) \(\mathstrut +\mathstrut 69540q^{11} \) \(\mathstrut +\mathstrut 79458q^{13} \) \(\mathstrut +\mathstrut 132500q^{15} \) \(\mathstrut -\mathstrut 127434q^{17} \) \(\mathstrut -\mathstrut 219972q^{19} \) \(\mathstrut +\mathstrut 2865848q^{21} \) \(\mathstrut -\mathstrut 808416q^{23} \) \(\mathstrut +\mathstrut 1171875q^{25} \) \(\mathstrut -\mathstrut 8154584q^{27} \) \(\mathstrut -\mathstrut 5365782q^{29} \) \(\mathstrut +\mathstrut 7615248q^{31} \) \(\mathstrut -\mathstrut 10547520q^{33} \) \(\mathstrut -\mathstrut 95000q^{35} \) \(\mathstrut +\mathstrut 8594538q^{37} \) \(\mathstrut +\mathstrut 4309208q^{39} \) \(\mathstrut +\mathstrut 21834438q^{41} \) \(\mathstrut -\mathstrut 32882700q^{43} \) \(\mathstrut -\mathstrut 32663125q^{45} \) \(\mathstrut +\mathstrut 78552936q^{47} \) \(\mathstrut +\mathstrut 71867331q^{49} \) \(\mathstrut -\mathstrut 5720904q^{51} \) \(\mathstrut -\mathstrut 78404454q^{53} \) \(\mathstrut -\mathstrut 84937500q^{55} \) \(\mathstrut +\mathstrut 208014032q^{57} \) \(\mathstrut +\mathstrut 27694356q^{59} \) \(\mathstrut +\mathstrut 289250466q^{61} \) \(\mathstrut -\mathstrut 723019072q^{63} \) \(\mathstrut -\mathstrut 174263750q^{65} \) \(\mathstrut -\mathstrut 26145732q^{67} \) \(\mathstrut -\mathstrut 165212376q^{69} \) \(\mathstrut +\mathstrut 728970504q^{71} \) \(\mathstrut -\mathstrut 549596802q^{73} \) \(\mathstrut -\mathstrut 120312500q^{75} \) \(\mathstrut +\mathstrut 81862320q^{77} \) \(\mathstrut +\mathstrut 450836304q^{79} \) \(\mathstrut +\mathstrut 2137918387q^{81} \) \(\mathstrut -\mathstrut 1909553076q^{83} \) \(\mathstrut -\mathstrut 474671250q^{85} \) \(\mathstrut +\mathstrut 585010632q^{87} \) \(\mathstrut -\mathstrut 632351058q^{89} \) \(\mathstrut +\mathstrut 1593068592q^{91} \) \(\mathstrut -\mathstrut 1451222128q^{93} \) \(\mathstrut -\mathstrut 309072500q^{95} \) \(\mathstrut +\mathstrut 1660769718q^{97} \) \(\mathstrut +\mathstrut 2052680340q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(20))\) 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
20.10.a.a \(1\) \(10.301\) \(\Q\) None \(0\) \(-48\) \(625\) \(-532\) \(-\) \(-\) \(q-48q^{3}+5^{4}q^{5}-532q^{7}-17379q^{9}+\cdots\)
20.10.a.b \(2\) \(10.301\) \(\Q(\sqrt{79}) \) None \(0\) \(-260\) \(-1250\) \(-380\) \(-\) \(+\) \(q+(-130+\beta )q^{3}-5^{4}q^{5}+(-190+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

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