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Properties

Label 38.6
Level 38
Weight 6
Dimension 75
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 540
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(540\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(38))\).

Total New Old
Modular forms 243 75 168
Cusp forms 207 75 132
Eisenstein series 36 0 36

Trace form

\( 75 q + O(q^{10}) \) \( 75 q + 864 q^{12} - 4344 q^{13} - 3960 q^{14} - 3564 q^{15} + 4302 q^{17} + 8748 q^{18} + 12810 q^{19} + 3168 q^{20} - 1890 q^{21} - 8532 q^{22} - 10278 q^{23} - 23364 q^{25} - 3960 q^{26} + 41157 q^{27} + 14304 q^{28} - 11358 q^{29} - 19638 q^{31} - 12906 q^{33} + 29556 q^{35} + 24642 q^{37} + 57726 q^{39} - 558 q^{41} - 2310 q^{43} + 32976 q^{44} - 118152 q^{45} - 60624 q^{46} - 177192 q^{47} - 25344 q^{48} - 65400 q^{49} - 115488 q^{50} + 45351 q^{51} + 2784 q^{52} + 105048 q^{53} + 123336 q^{54} + 205992 q^{55} + 112896 q^{56} + 277110 q^{57} + 96624 q^{58} + 177210 q^{59} + 35136 q^{60} + 21126 q^{61} - 84024 q^{62} - 268416 q^{63} - 24576 q^{64} - 545760 q^{65} - 391968 q^{66} - 372066 q^{67} - 36144 q^{68} - 89694 q^{69} + 77616 q^{70} + 452016 q^{71} + 138816 q^{72} + 274017 q^{73} + 236250 q^{75} + 498816 q^{77} + 421776 q^{78} + 241086 q^{79} - 452097 q^{81} - 286704 q^{82} - 553464 q^{83} - 439776 q^{84} - 494568 q^{85} - 180720 q^{86} - 739980 q^{87} - 6876 q^{89} + 363240 q^{90} + 519456 q^{91} + 265536 q^{92} + 1344798 q^{93} + 636192 q^{94} + 1251810 q^{95} + 387198 q^{97} + 371232 q^{98} - 197541 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.6.a \(\chi_{38}(1, \cdot)\) 38.6.a.a 1 1
38.6.a.b 1
38.6.a.c 2
38.6.a.d 3
38.6.c \(\chi_{38}(7, \cdot)\) 38.6.c.a 6 2
38.6.c.b 8
38.6.e \(\chi_{38}(5, \cdot)\) 38.6.e.a 24 6
38.6.e.b 30

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)