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Properties

Label 38.5
Level 38
Weight 5
Dimension 60
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 450
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(450\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(38))\).

Total New Old
Modular forms 198 60 138
Cusp forms 162 60 102
Eisenstein series 36 0 36

Trace form

\( 60 q + O(q^{10}) \) \( 60 q - 432 q^{12} + 120 q^{13} + 864 q^{14} + 2268 q^{15} + 594 q^{17} - 1554 q^{19} - 1296 q^{20} - 4158 q^{21} - 3024 q^{22} - 1890 q^{23} - 252 q^{25} + 1728 q^{26} + 1692 q^{27} + 2640 q^{28} - 864 q^{29} + 2808 q^{31} + 10800 q^{33} + 4752 q^{35} - 7992 q^{39} - 4752 q^{41} - 17274 q^{43} - 6048 q^{44} - 29646 q^{45} - 2880 q^{46} + 7398 q^{47} + 2304 q^{48} + 24342 q^{49} + 27648 q^{50} + 46494 q^{51} + 2112 q^{52} + 20952 q^{53} + 11232 q^{54} + 7848 q^{55} - 10170 q^{57} - 8064 q^{58} - 29430 q^{59} - 14976 q^{60} - 41136 q^{61} - 28512 q^{62} - 43992 q^{63} - 3072 q^{64} - 34290 q^{65} - 23040 q^{66} + 14154 q^{67} + 864 q^{68} + 21762 q^{69} + 28224 q^{70} + 76302 q^{71} + 16128 q^{72} + 22254 q^{73} - 46710 q^{77} - 57600 q^{78} - 60036 q^{79} - 26964 q^{81} + 8640 q^{82} + 12042 q^{83} + 36720 q^{84} + 57672 q^{85} + 31104 q^{86} + 113040 q^{87} + 45846 q^{89} + 59040 q^{90} + 65784 q^{91} + 12960 q^{92} + 41544 q^{93} - 97038 q^{95} - 65682 q^{97} - 51840 q^{98} - 122796 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(38))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
38.5.b \(\chi_{38}(37, \cdot)\) 38.5.b.a 8 1
38.5.d \(\chi_{38}(27, \cdot)\) 38.5.d.a 16 2
38.5.f \(\chi_{38}(3, \cdot)\) 38.5.f.a 36 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)