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Properties

Label 138.4
Level 138
Weight 4
Dimension 394
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 4224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(4224\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(138))\).

Total New Old
Modular forms 1672 394 1278
Cusp forms 1496 394 1102
Eisenstein series 176 0 176

Trace form

\( 394 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + O(q^{10}) \) \( 394 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + 24 q^{10} - 24 q^{11} + 24 q^{12} - 76 q^{13} - 64 q^{14} - 712 q^{15} - 32 q^{16} - 100 q^{17} + 124 q^{18} + 400 q^{19} + 656 q^{20} + 1224 q^{21} + 1016 q^{22} + 1768 q^{23} - 48 q^{24} + 1586 q^{25} + 592 q^{26} + 186 q^{27} - 224 q^{28} - 940 q^{29} - 1568 q^{30} - 2024 q^{31} + 64 q^{32} - 1864 q^{33} - 504 q^{34} - 2668 q^{35} - 72 q^{36} - 2884 q^{37} + 80 q^{38} + 360 q^{39} + 96 q^{40} + 1016 q^{41} + 192 q^{42} + 3536 q^{43} - 96 q^{44} - 108 q^{45} + 336 q^{46} + 3976 q^{47} + 96 q^{48} + 4530 q^{49} - 356 q^{50} - 96 q^{51} - 304 q^{52} - 880 q^{53} + 3016 q^{54} - 4104 q^{55} - 256 q^{56} + 516 q^{57} + 120 q^{58} - 4708 q^{59} + 232 q^{60} + 1076 q^{61} - 352 q^{62} - 3892 q^{63} - 128 q^{64} - 456 q^{65} - 5600 q^{66} - 1768 q^{67} + 1008 q^{68} - 6976 q^{69} - 384 q^{70} - 1584 q^{71} - 2320 q^{72} - 436 q^{73} + 1016 q^{74} - 8520 q^{75} - 160 q^{76} + 384 q^{77} + 996 q^{78} - 1820 q^{79} - 192 q^{80} + 6746 q^{81} + 168 q^{82} + 1820 q^{83} + 3400 q^{84} + 3668 q^{85} - 208 q^{86} + 4866 q^{87} + 192 q^{88} + 2120 q^{89} + 216 q^{90} + 9224 q^{91} - 672 q^{92} - 528 q^{93} - 384 q^{94} - 4992 q^{95} - 192 q^{96} - 24968 q^{97} - 14252 q^{98} - 3450 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.4.a \(\chi_{138}(1, \cdot)\) 138.4.a.a 1 1
138.4.a.b 1
138.4.a.c 1
138.4.a.d 2
138.4.a.e 2
138.4.a.f 3
138.4.d \(\chi_{138}(137, \cdot)\) 138.4.d.a 24 1
138.4.e \(\chi_{138}(13, \cdot)\) 138.4.e.a 30 10
138.4.e.b 30
138.4.e.c 30
138.4.e.d 30
138.4.f \(\chi_{138}(5, \cdot)\) 138.4.f.a 240 10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)