Properties

Label 20.10
Level 20
Weight 10
Dimension 57
Nonzero newspaces 3
Newforms 5
Sturm bound 240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(20))\).

Total New Old
Modular forms 118 65 53
Cusp forms 98 57 41
Eisenstein series 20 8 12

Trace form

\(57q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 308q^{3} \) \(\mathstrut +\mathstrut 31q^{5} \) \(\mathstrut +\mathstrut 6152q^{6} \) \(\mathstrut -\mathstrut 912q^{7} \) \(\mathstrut -\mathstrut 716q^{8} \) \(\mathstrut +\mathstrut 8459q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(57q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 308q^{3} \) \(\mathstrut +\mathstrut 31q^{5} \) \(\mathstrut +\mathstrut 6152q^{6} \) \(\mathstrut -\mathstrut 912q^{7} \) \(\mathstrut -\mathstrut 716q^{8} \) \(\mathstrut +\mathstrut 8459q^{9} \) \(\mathstrut +\mathstrut 11446q^{10} \) \(\mathstrut +\mathstrut 34740q^{11} \) \(\mathstrut -\mathstrut 155360q^{12} \) \(\mathstrut -\mathstrut 6704q^{13} \) \(\mathstrut +\mathstrut 32740q^{15} \) \(\mathstrut +\mathstrut 3000q^{16} \) \(\mathstrut -\mathstrut 637428q^{17} \) \(\mathstrut -\mathstrut 679086q^{18} \) \(\mathstrut -\mathstrut 447636q^{19} \) \(\mathstrut -\mathstrut 334324q^{20} \) \(\mathstrut +\mathstrut 1944376q^{21} \) \(\mathstrut +\mathstrut 3176920q^{22} \) \(\mathstrut -\mathstrut 808416q^{23} \) \(\mathstrut +\mathstrut 5274381q^{25} \) \(\mathstrut -\mathstrut 11222732q^{26} \) \(\mathstrut -\mathstrut 8154584q^{27} \) \(\mathstrut +\mathstrut 12731840q^{28} \) \(\mathstrut +\mathstrut 899874q^{29} \) \(\mathstrut +\mathstrut 15498680q^{30} \) \(\mathstrut +\mathstrut 7989712q^{31} \) \(\mathstrut -\mathstrut 29092792q^{32} \) \(\mathstrut -\mathstrut 13035520q^{33} \) \(\mathstrut -\mathstrut 8209160q^{35} \) \(\mathstrut +\mathstrut 44773372q^{36} \) \(\mathstrut +\mathstrut 6991724q^{37} \) \(\mathstrut -\mathstrut 26115120q^{38} \) \(\mathstrut +\mathstrut 27695864q^{39} \) \(\mathstrut -\mathstrut 55995604q^{40} \) \(\mathstrut +\mathstrut 552302q^{41} \) \(\mathstrut +\mathstrut 82830200q^{42} \) \(\mathstrut -\mathstrut 32882700q^{43} \) \(\mathstrut -\mathstrut 54538499q^{45} \) \(\mathstrut -\mathstrut 92534488q^{46} \) \(\mathstrut +\mathstrut 78552936q^{47} \) \(\mathstrut +\mathstrut 46448320q^{48} \) \(\mathstrut +\mathstrut 216766143q^{49} \) \(\mathstrut -\mathstrut 54429014q^{50} \) \(\mathstrut -\mathstrut 114424456q^{51} \) \(\mathstrut +\mathstrut 88926156q^{52} \) \(\mathstrut -\mathstrut 274039236q^{53} \) \(\mathstrut -\mathstrut 282892300q^{55} \) \(\mathstrut -\mathstrut 177356448q^{56} \) \(\mathstrut +\mathstrut 270379472q^{57} \) \(\mathstrut +\mathstrut 82723048q^{58} \) \(\mathstrut +\mathstrut 466689828q^{59} \) \(\mathstrut +\mathstrut 166923520q^{60} \) \(\mathstrut +\mathstrut 366448194q^{61} \) \(\mathstrut -\mathstrut 292810200q^{62} \) \(\mathstrut -\mathstrut 723019072q^{63} \) \(\mathstrut -\mathstrut 526945428q^{65} \) \(\mathstrut +\mathstrut 614341200q^{66} \) \(\mathstrut -\mathstrut 26145732q^{67} \) \(\mathstrut -\mathstrut 289868412q^{68} \) \(\mathstrut +\mathstrut 1021502632q^{69} \) \(\mathstrut -\mathstrut 203227600q^{70} \) \(\mathstrut +\mathstrut 224888616q^{71} \) \(\mathstrut +\mathstrut 930217668q^{72} \) \(\mathstrut -\mathstrut 44807784q^{73} \) \(\mathstrut -\mathstrut 1158654100q^{75} \) \(\mathstrut -\mathstrut 1061841600q^{76} \) \(\mathstrut -\mathstrut 195453840q^{77} \) \(\mathstrut +\mathstrut 49362600q^{78} \) \(\mathstrut +\mathstrut 2245791312q^{79} \) \(\mathstrut +\mathstrut 210150736q^{80} \) \(\mathstrut -\mathstrut 552782283q^{81} \) \(\mathstrut -\mathstrut 591442904q^{82} \) \(\mathstrut -\mathstrut 1909553076q^{83} \) \(\mathstrut -\mathstrut 538201268q^{85} \) \(\mathstrut -\mathstrut 874588728q^{86} \) \(\mathstrut +\mathstrut 585010632q^{87} \) \(\mathstrut +\mathstrut 865939360q^{88} \) \(\mathstrut +\mathstrut 1748967126q^{89} \) \(\mathstrut +\mathstrut 1779829206q^{90} \) \(\mathstrut +\mathstrut 781823568q^{91} \) \(\mathstrut -\mathstrut 1106673600q^{92} \) \(\mathstrut -\mathstrut 4005699248q^{93} \) \(\mathstrut -\mathstrut 2253979460q^{95} \) \(\mathstrut +\mathstrut 1870685312q^{96} \) \(\mathstrut +\mathstrut 5101092544q^{97} \) \(\mathstrut -\mathstrut 3885590026q^{98} \) \(\mathstrut +\mathstrut 4822342340q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(20))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
20.10.a \(\chi_{20}(1, \cdot)\) 20.10.a.a 1 1
20.10.a.b 2
20.10.c \(\chi_{20}(9, \cdot)\) 20.10.c.a 4 1
20.10.e \(\chi_{20}(3, \cdot)\) 20.10.e.a 2 2
20.10.e.b 48

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)