Properties

Label 20.10.a
Level 20
Weight 10
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces

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

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