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

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

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 the 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

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