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Properties

Label 38.11
Level 38
Weight 11
Dimension 150
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 990
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(990\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(38))\).

Total New Old
Modular forms 468 150 318
Cusp forms 432 150 282
Eisenstein series 36 0 36

Trace form

\( 150 q + O(q^{10}) \) \( 150 q + 746496 q^{12} - 3366600 q^{13} + 1837440 q^{14} + 5677452 q^{15} - 5855022 q^{17} + 21917910 q^{19} + 10238976 q^{20} - 7603470 q^{21} - 31261248 q^{22} - 20299050 q^{23} + 97965252 q^{25} + 26737920 q^{26} - 149099706 q^{27} - 11443200 q^{28} - 88955856 q^{29} + 61388388 q^{31} + 158021064 q^{33} - 321628392 q^{35} + 789807132 q^{39} - 12010392 q^{41} - 1894698426 q^{43} + 500179968 q^{44} + 678263058 q^{45} - 1467100800 q^{46} - 1005470694 q^{47} + 51904512 q^{48} + 615004638 q^{49} + 3323282688 q^{50} + 3958076664 q^{51} - 107083776 q^{52} - 3700105704 q^{53} - 3334018752 q^{54} - 3059187192 q^{55} + 4422952710 q^{57} + 3029355648 q^{58} + 7884604530 q^{59} + 1891160064 q^{60} + 496162164 q^{61} - 4716771264 q^{62} - 13380082776 q^{63} - 805306368 q^{64} - 6827534190 q^{65} + 4782009600 q^{66} + 14557764210 q^{67} + 2213747712 q^{68} + 6925004658 q^{69} - 6176370816 q^{70} - 28053373698 q^{71} - 1563623424 q^{72} + 6121794732 q^{73} - 8116451370 q^{77} + 26210847744 q^{78} + 24896102340 q^{79} - 42208937262 q^{81} - 16115058432 q^{82} - 14308495038 q^{83} + 14424652800 q^{84} + 36770636232 q^{85} + 19598722560 q^{86} + 70064036064 q^{87} - 805675590 q^{89} - 48755525760 q^{90} - 62083305384 q^{91} - 21506291712 q^{92} - 57688041492 q^{93} + 74399907186 q^{95} + 50591961918 q^{97} + 60044548608 q^{98} - 4123224810 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(38))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
38.11.b \(\chi_{38}(37, \cdot)\) 38.11.b.a 18 1
38.11.d \(\chi_{38}(27, \cdot)\) 38.11.d.a 36 2
38.11.f \(\chi_{38}(3, \cdot)\) 38.11.f.a 96 6

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 1}\)