# Properties

 Label 74.3 Level 74 Weight 3 Dimension 114 Nonzero newspaces 3 Newform subspaces 8 Sturm bound 1026 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$74 = 2 \cdot 37$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$3$$ Newform subspaces: $$8$$ Sturm bound: $$1026$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(74))$$.

Total New Old
Modular forms 378 114 264
Cusp forms 306 114 192
Eisenstein series 72 0 72

## Trace form

 $$114 q + O(q^{10})$$ $$114 q - 90 q^{26} - 432 q^{27} - 96 q^{28} - 252 q^{29} - 432 q^{30} - 540 q^{31} - 216 q^{33} - 144 q^{34} - 108 q^{35} + 84 q^{37} + 72 q^{38} + 252 q^{39} + 180 q^{40} + 540 q^{41} + 432 q^{42} + 504 q^{43} + 972 q^{45} + 720 q^{46} + 396 q^{47} + 144 q^{48} + 624 q^{49} + 126 q^{50} - 504 q^{59} - 540 q^{61} - 1080 q^{63} - 648 q^{65} - 216 q^{67} - 576 q^{69} - 144 q^{71} + 360 q^{75} + 288 q^{77} + 432 q^{79} + 1152 q^{81} + 360 q^{83} + 972 q^{85} + 1512 q^{87} + 720 q^{89} + 420 q^{91} - 648 q^{92} - 1836 q^{93} - 1152 q^{94} - 2160 q^{95} - 1872 q^{97} - 1728 q^{98} - 1980 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(74))$$

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
74.3.d $$\chi_{74}(31, \cdot)$$ 74.3.d.a 2 2
74.3.d.b 2
74.3.d.c 2
74.3.d.d 4
74.3.g $$\chi_{74}(23, \cdot)$$ 74.3.g.a 8 4
74.3.g.b 12
74.3.i $$\chi_{74}(5, \cdot)$$ 74.3.i.a 36 12
74.3.i.b 48

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(74))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(74)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 2}$$