Properties

Label 20.10
Level 20
Weight 10
Dimension 57
Nonzero newspaces 3
Newform subspaces 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: \( 3 \)
Newform subspaces: \( 5 \)
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

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

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

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