Properties

Label 38.9
Level 38
Weight 9
Dimension 120
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 810
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(810\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(38))\).

Total New Old
Modular forms 378 120 258
Cusp forms 342 120 222
Eisenstein series 36 0 36

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 62208 q^{12} - 40440 q^{13} - 214272 q^{14} - 20412 q^{15} + 303534 q^{17} - 1005438 q^{19} - 642816 q^{20} - 860706 q^{21} + 556416 q^{22} + 1166130 q^{23} + 314748 q^{25} - 2087424 q^{26} - 6975648 q^{27} + 971520 q^{28} + 1422144 q^{29} - 3498768 q^{31} + 3477600 q^{33} + 9057312 q^{35} - 19452528 q^{39} - 4723488 q^{41} - 7720134 q^{43} + 4451328 q^{44} + 94777614 q^{45} + 12003840 q^{46} - 31577742 q^{47} - 8257536 q^{48} - 61276902 q^{49} - 24993792 q^{50} + 68231646 q^{51} + 4933632 q^{52} + 79429032 q^{53} + 55980288 q^{54} + 45761688 q^{55} - 63776070 q^{57} - 46900224 q^{58} - 144766170 q^{59} - 54153216 q^{60} - 56466984 q^{61} - 1596672 q^{62} + 117436248 q^{63} + 12582912 q^{64} + 199314810 q^{65} + 177131520 q^{66} - 29305626 q^{67} - 7934976 q^{68} - 186304482 q^{69} - 188084736 q^{70} - 162102222 q^{71} + 35094528 q^{72} + 215703534 q^{73} - 320487570 q^{77} + 124876800 q^{78} + 105924948 q^{79} + 29439648 q^{81} - 112734720 q^{82} - 264600378 q^{83} - 348399360 q^{84} - 376540488 q^{85} - 97293312 q^{86} + 245886480 q^{87} + 242203122 q^{89} + 631491840 q^{90} + 184478280 q^{91} + 200517120 q^{92} + 476957664 q^{93} - 172188018 q^{95} + 73003698 q^{97} - 683873280 q^{98} - 1320901992 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(38))\)

We only show spaces with odd 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
38.9.b \(\chi_{38}(37, \cdot)\) 38.9.b.a 12 1
38.9.d \(\chi_{38}(27, \cdot)\) 38.9.d.a 24 2
38.9.f \(\chi_{38}(3, \cdot)\) 38.9.f.a 84 6

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)