Properties

Label 20.7
Level 20
Weight 7
Dimension 34
Nonzero newspaces 3
Newforms 6
Sturm bound 168
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 6 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(20))\).

Total New Old
Modular forms 82 38 44
Cusp forms 62 34 28
Eisenstein series 20 4 16

Trace form

\(34q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut +\mathstrut 32q^{3} \) \(\mathstrut +\mathstrut 220q^{4} \) \(\mathstrut -\mathstrut 180q^{5} \) \(\mathstrut -\mathstrut 640q^{6} \) \(\mathstrut -\mathstrut 264q^{7} \) \(\mathstrut +\mathstrut 440q^{8} \) \(\mathstrut +\mathstrut 916q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut +\mathstrut 32q^{3} \) \(\mathstrut +\mathstrut 220q^{4} \) \(\mathstrut -\mathstrut 180q^{5} \) \(\mathstrut -\mathstrut 640q^{6} \) \(\mathstrut -\mathstrut 264q^{7} \) \(\mathstrut +\mathstrut 440q^{8} \) \(\mathstrut +\mathstrut 916q^{9} \) \(\mathstrut +\mathstrut 2046q^{10} \) \(\mathstrut +\mathstrut 2200q^{11} \) \(\mathstrut -\mathstrut 440q^{12} \) \(\mathstrut -\mathstrut 4182q^{13} \) \(\mathstrut -\mathstrut 1624q^{14} \) \(\mathstrut -\mathstrut 7768q^{15} \) \(\mathstrut -\mathstrut 1232q^{16} \) \(\mathstrut +\mathstrut 3562q^{17} \) \(\mathstrut +\mathstrut 15790q^{18} \) \(\mathstrut -\mathstrut 18284q^{20} \) \(\mathstrut +\mathstrut 10816q^{21} \) \(\mathstrut -\mathstrut 26160q^{22} \) \(\mathstrut +\mathstrut 19984q^{23} \) \(\mathstrut +\mathstrut 52656q^{24} \) \(\mathstrut +\mathstrut 12382q^{25} \) \(\mathstrut -\mathstrut 30684q^{26} \) \(\mathstrut -\mathstrut 115528q^{27} \) \(\mathstrut +\mathstrut 19320q^{28} \) \(\mathstrut -\mathstrut 65080q^{29} \) \(\mathstrut -\mathstrut 17480q^{30} \) \(\mathstrut +\mathstrut 104976q^{31} \) \(\mathstrut -\mathstrut 60800q^{32} \) \(\mathstrut +\mathstrut 290200q^{33} \) \(\mathstrut +\mathstrut 149004q^{34} \) \(\mathstrut -\mathstrut 116072q^{35} \) \(\mathstrut -\mathstrut 25732q^{36} \) \(\mathstrut -\mathstrut 178914q^{37} \) \(\mathstrut +\mathstrut 74800q^{38} \) \(\mathstrut +\mathstrut 65256q^{40} \) \(\mathstrut +\mathstrut 163832q^{41} \) \(\mathstrut -\mathstrut 138360q^{42} \) \(\mathstrut +\mathstrut 60720q^{43} \) \(\mathstrut -\mathstrut 387280q^{44} \) \(\mathstrut -\mathstrut 399190q^{45} \) \(\mathstrut -\mathstrut 439960q^{46} \) \(\mathstrut -\mathstrut 355248q^{47} \) \(\mathstrut +\mathstrut 297600q^{48} \) \(\mathstrut +\mathstrut 296916q^{49} \) \(\mathstrut +\mathstrut 97486q^{50} \) \(\mathstrut +\mathstrut 641872q^{51} \) \(\mathstrut +\mathstrut 548280q^{52} \) \(\mathstrut +\mathstrut 668686q^{53} \) \(\mathstrut +\mathstrut 368272q^{54} \) \(\mathstrut -\mathstrut 310200q^{55} \) \(\mathstrut +\mathstrut 295120q^{56} \) \(\mathstrut -\mathstrut 1326256q^{57} \) \(\mathstrut +\mathstrut 350700q^{58} \) \(\mathstrut -\mathstrut 745400q^{60} \) \(\mathstrut +\mathstrut 203768q^{61} \) \(\mathstrut -\mathstrut 7120q^{62} \) \(\mathstrut +\mathstrut 2288q^{63} \) \(\mathstrut -\mathstrut 549440q^{64} \) \(\mathstrut +\mathstrut 426590q^{65} \) \(\mathstrut -\mathstrut 1468720q^{66} \) \(\mathstrut -\mathstrut 230304q^{67} \) \(\mathstrut -\mathstrut 1678280q^{68} \) \(\mathstrut -\mathstrut 294248q^{69} \) \(\mathstrut +\mathstrut 1218080q^{70} \) \(\mathstrut +\mathstrut 174128q^{71} \) \(\mathstrut +\mathstrut 2317560q^{72} \) \(\mathstrut -\mathstrut 747522q^{73} \) \(\mathstrut +\mathstrut 1917444q^{74} \) \(\mathstrut +\mathstrut 1855048q^{75} \) \(\mathstrut +\mathstrut 2723520q^{76} \) \(\mathstrut +\mathstrut 1694360q^{77} \) \(\mathstrut +\mathstrut 473200q^{78} \) \(\mathstrut -\mathstrut 1375504q^{80} \) \(\mathstrut -\mathstrut 1971498q^{81} \) \(\mathstrut -\mathstrut 3169500q^{82} \) \(\mathstrut -\mathstrut 2190936q^{83} \) \(\mathstrut -\mathstrut 4782688q^{84} \) \(\mathstrut -\mathstrut 698022q^{85} \) \(\mathstrut -\mathstrut 5052880q^{86} \) \(\mathstrut +\mathstrut 2614304q^{87} \) \(\mathstrut -\mathstrut 278880q^{88} \) \(\mathstrut -\mathstrut 287720q^{89} \) \(\mathstrut +\mathstrut 1932966q^{90} \) \(\mathstrut -\mathstrut 2186976q^{91} \) \(\mathstrut +\mathstrut 4095720q^{92} \) \(\mathstrut -\mathstrut 3403928q^{93} \) \(\mathstrut +\mathstrut 8576456q^{94} \) \(\mathstrut +\mathstrut 3484184q^{95} \) \(\mathstrut +\mathstrut 7915520q^{96} \) \(\mathstrut +\mathstrut 5683086q^{97} \) \(\mathstrut +\mathstrut 1050270q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)

We only show spaces with odd 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
20.7.b \(\chi_{20}(11, \cdot)\) 20.7.b.a 12 1
20.7.d \(\chi_{20}(19, \cdot)\) 20.7.d.a 1 1
20.7.d.b 1
20.7.d.c 2
20.7.d.d 12
20.7.f \(\chi_{20}(13, \cdot)\) 20.7.f.a 6 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)