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Properties

Label 138.3
Level 138
Weight 3
Dimension 264
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 3168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(3168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(138))\).

Total New Old
Modular forms 1144 264 880
Cusp forms 968 264 704
Eisenstein series 176 0 176

Trace form

\( 264 q + O(q^{10}) \) \( 264 q + 154 q^{15} + 220 q^{17} + 176 q^{18} + 132 q^{19} + 88 q^{20} + 66 q^{21} - 88 q^{23} - 264 q^{25} - 176 q^{26} - 330 q^{27} - 264 q^{28} - 308 q^{29} - 352 q^{30} - 396 q^{31} - 242 q^{33} + 440 q^{35} + 704 q^{37} + 264 q^{39} + 176 q^{41} + 176 q^{43} - 176 q^{47} - 528 q^{49} - 264 q^{51} - 352 q^{53} - 308 q^{54} - 880 q^{55} - 1254 q^{57} - 616 q^{59} - 176 q^{60} - 550 q^{63} - 176 q^{66} + 110 q^{69} + 176 q^{72} + 1430 q^{75} + 660 q^{78} + 528 q^{79} + 1584 q^{81} + 352 q^{83} + 352 q^{84} + 264 q^{85} + 264 q^{87} + 88 q^{89} + 484 q^{95} + 1980 q^{97} + 1408 q^{98} + 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.3.b \(\chi_{138}(91, \cdot)\) 138.3.b.a 8 1
138.3.c \(\chi_{138}(47, \cdot)\) 138.3.c.a 16 1
138.3.g \(\chi_{138}(29, \cdot)\) 138.3.g.a 160 10
138.3.h \(\chi_{138}(7, \cdot)\) 138.3.h.a 80 10

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)