Properties

Label 38.7
Level 38
Weight 7
Dimension 90
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 630
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(630\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(38))\).

Total New Old
Modular forms 288 90 198
Cusp forms 252 90 162
Eisenstein series 36 0 36

Trace form

\( 90q + O(q^{10}) \) \( 90q + 20160q^{13} + 3744q^{14} - 23328q^{15} - 14400q^{17} + 42336q^{19} + 32256q^{20} + 81648q^{21} + 32400q^{22} - 7920q^{23} - 157248q^{25} - 76608q^{26} - 124830q^{27} + 69120q^{28} + 115920q^{29} + 30780q^{31} - 304776q^{33} - 225432q^{35} + 427140q^{39} + 192600q^{41} - 252504q^{43} - 129600q^{44} + 49248q^{45} + 738720q^{46} + 600300q^{47} + 92160q^{48} - 61560q^{49} - 689472q^{50} - 711990q^{51} - 120960q^{52} - 1425600q^{53} - 853200q^{54} - 637632q^{55} + 856800q^{57} + 660960q^{58} + 2268000q^{59} + 1039104q^{60} + 1900260q^{61} + 1263600q^{62} + 2037600q^{63} - 878940q^{65} - 2399040q^{66} - 2114208q^{67} - 492480q^{68} - 2667600q^{69} - 889056q^{70} + 716760q^{71} + 1059840q^{72} + 741150q^{73} - 3166020q^{77} - 2255616q^{78} + 3285144q^{79} + 7604262q^{81} + 2731968q^{82} + 3395376q^{83} + 1313280q^{84} - 451008q^{85} - 1229184q^{86} - 11001456q^{87} - 6096204q^{89} - 6766560q^{90} - 5753088q^{91} - 1723392q^{92} - 2560284q^{93} - 4345704q^{95} + 7225632q^{97} + 6565248q^{98} + 23133114q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.7.b \(\chi_{38}(37, \cdot)\) 38.7.b.a 10 1
38.7.d \(\chi_{38}(27, \cdot)\) 38.7.d.a 20 2
38.7.f \(\chi_{38}(3, \cdot)\) 38.7.f.a 60 6

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)