Properties

Label 38.4
Level 38
Weight 4
Dimension 45
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(38))\).

Total New Old
Modular forms 153 45 108
Cusp forms 117 45 72
Eisenstein series 36 0 36

Trace form

\( 45q + O(q^{10}) \) \( 45q + 144q^{12} + 288q^{13} + 36q^{14} - 216q^{15} - 288q^{17} - 486q^{18} - 756q^{19} - 288q^{20} - 504q^{21} - 162q^{22} + 36q^{23} + 864q^{25} + 684q^{26} + 1953q^{27} + 432q^{28} + 630q^{29} + 90q^{31} - 918q^{33} - 1116q^{35} - 666q^{37} - 1890q^{39} - 450q^{41} + 504q^{43} + 900q^{44} + 5130q^{45} + 1944q^{46} + 2790q^{47} + 144q^{48} + 1710q^{49} - 1008q^{50} - 1035q^{51} - 216q^{52} - 3168q^{53} - 2700q^{54} - 3888q^{55} - 2016q^{56} - 5040q^{57} - 1944q^{58} - 4500q^{59} - 1584q^{60} - 1782q^{61} - 1404q^{62} + 936q^{63} + 2070q^{65} + 2448q^{66} + 2160q^{67} + 684q^{68} + 5400q^{69} + 4536q^{70} + 7326q^{71} + 1656q^{72} - 567q^{73} - 3150q^{75} + 2502q^{77} + 6408q^{78} + 2610q^{79} + 5121q^{81} + 2232q^{82} + 1710q^{83} + 864q^{84} - 288q^{85} - 792q^{86} - 3420q^{87} - 1530q^{89} - 6660q^{90} - 1944q^{91} - 3168q^{92} - 11862q^{93} - 6768q^{94} + 3168q^{95} + 972q^{97} - 5904q^{98} - 4545q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)

We only show spaces with even 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
38.4.a \(\chi_{38}(1, \cdot)\) 38.4.a.a 1 1
38.4.a.b 2
38.4.a.c 2
38.4.c \(\chi_{38}(7, \cdot)\) 38.4.c.a 2 2
38.4.c.b 2
38.4.c.c 6
38.4.e \(\chi_{38}(5, \cdot)\) 38.4.e.a 12 6
38.4.e.b 18

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)