Properties

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

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
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

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

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

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