Properties

Label 20.10.a
Level $20$
Weight $10$
Character orbit 20.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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
20.10.a.a 20.a 1.a $1$ $10.301$ \(\Q\) None \(0\) \(-48\) \(625\) \(-532\) $-$ $-$ $\mathrm{SU}(2)$ \(q-48q^{3}+5^{4}q^{5}-532q^{7}-17379q^{9}+\cdots\)
20.10.a.b 20.a 1.a $2$ $10.301$ \(\Q(\sqrt{79}) \) None \(0\) \(-260\) \(-1250\) \(-380\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-130+\beta )q^{3}-5^{4}q^{5}+(-190+\cdots)q^{7}+\cdots\)

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

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