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Properties

Label 38.8
Level 38
Weight 8
Dimension 103
Nonzero newspaces 3
Newform subspaces 9
Sturm bound 720
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 9 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(38))\).

Total New Old
Modular forms 333 103 230
Cusp forms 297 103 194
Eisenstein series 36 0 36

Trace form

\( 103 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} + O(q^{10}) \) \( 103 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} - 3360 q^{10} - 2184 q^{11} - 11904 q^{12} - 47092 q^{13} + 56720 q^{14} + 128484 q^{15} - 8192 q^{16} - 88146 q^{17} - 190152 q^{18} - 161114 q^{19} + 28032 q^{20} + 260250 q^{21} + 334776 q^{22} + 59370 q^{23} + 12288 q^{24} - 448586 q^{25} - 487792 q^{26} + 238581 q^{27} + 160640 q^{28} - 392838 q^{29} - 40320 q^{30} - 31006 q^{31} + 65536 q^{32} + 1618794 q^{33} + 235296 q^{34} - 156876 q^{35} + 261504 q^{36} - 1232806 q^{37} - 319520 q^{38} - 1430202 q^{39} - 215040 q^{40} + 771594 q^{41} + 195072 q^{42} + 7315082 q^{43} - 35520 q^{44} - 7155540 q^{45} - 3499104 q^{46} - 5451648 q^{47} + 380928 q^{48} + 2048454 q^{49} + 9366832 q^{50} + 15820695 q^{51} + 162176 q^{52} + 1697292 q^{53} - 5765904 q^{54} - 10233288 q^{55} - 5281792 q^{56} - 14459190 q^{57} - 5923392 q^{58} - 8932710 q^{59} + 2370816 q^{60} + 9358190 q^{61} + 16431920 q^{62} + 15379344 q^{63} + 1048576 q^{64} + 16772880 q^{65} + 2089152 q^{66} + 4173134 q^{67} - 5334336 q^{68} - 30139002 q^{69} - 21293664 q^{70} - 3690000 q^{71} + 4870656 q^{72} + 5856455 q^{73} + 2568416 q^{74} - 16902150 q^{75} + 2556160 q^{76} + 24529128 q^{77} + 3456672 q^{78} - 16747138 q^{79} + 1720320 q^{80} - 41281821 q^{81} - 9100416 q^{82} + 6859632 q^{83} + 22247808 q^{84} + 52273872 q^{85} + 15283424 q^{86} + 89110980 q^{87} + 1118208 q^{88} + 18620928 q^{89} + 1239120 q^{90} - 53284736 q^{91} - 29777664 q^{92} - 106636638 q^{93} - 52239552 q^{94} - 21696582 q^{95} + 786432 q^{96} - 94148962 q^{97} - 6780336 q^{98} - 24494085 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.8.a \(\chi_{38}(1, \cdot)\) 38.8.a.a 1 1
38.8.a.b 2
38.8.a.c 2
38.8.a.d 2
38.8.a.e 4
38.8.c \(\chi_{38}(7, \cdot)\) 38.8.c.a 12 2
38.8.c.b 14
38.8.e \(\chi_{38}(5, \cdot)\) 38.8.e.a 30 6
38.8.e.b 36

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)