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

\( 45 q + 144 q^{12} + 288 q^{13} + 36 q^{14} - 216 q^{15} - 288 q^{17} - 486 q^{18} - 756 q^{19} - 288 q^{20} - 504 q^{21} - 162 q^{22} + 36 q^{23} + 864 q^{25} + 684 q^{26} + 1953 q^{27} + 432 q^{28} + 630 q^{29}+ \cdots - 4545 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 available 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

\( S_{4}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)