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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

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

Display 100 coefficients 10 coefficients

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 available 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

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