# Properties

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

## 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

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

## 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 the 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

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