# Properties

 Label 32.7 Level 32 Weight 7 Dimension 103 Nonzero newspaces 3 Newform subspaces 5 Sturm bound 448 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$32 = 2^{5}$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$448$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(32))$$.

Total New Old
Modular forms 208 113 95
Cusp forms 176 103 73
Eisenstein series 32 10 22

## Trace form

 $$103 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 40 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 1655 q^{9} + O(q^{10})$$ $$103 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 40 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 1655 q^{9} + 2996 q^{10} + 1358 q^{11} - 3892 q^{12} - 4216 q^{13} - 8532 q^{14} - 8 q^{15} + 14096 q^{16} + 2934 q^{17} + 24296 q^{18} + 3934 q^{19} - 14004 q^{20} - 3396 q^{21} - 19552 q^{22} + 13116 q^{23} - 43568 q^{24} + 2059 q^{25} + 5296 q^{26} - 101504 q^{27} + 85496 q^{28} + 35592 q^{29} + 102980 q^{30} - 58904 q^{32} + 30860 q^{33} - 139248 q^{34} + 212252 q^{35} - 328464 q^{36} + 126056 q^{37} + 457684 q^{38} - 254404 q^{39} + 430952 q^{40} - 166494 q^{41} - 256504 q^{42} + 22894 q^{43} - 808764 q^{44} - 468188 q^{45} - 197284 q^{46} - 8 q^{47} + 349488 q^{48} + 382907 q^{49} + 1254548 q^{50} + 307620 q^{51} - 71644 q^{52} + 718152 q^{53} - 455840 q^{54} - 232708 q^{55} - 619736 q^{56} - 578576 q^{57} - 290272 q^{58} + 39150 q^{59} + 803000 q^{60} - 956536 q^{61} + 1415352 q^{62} - 1533928 q^{64} + 632016 q^{65} - 308980 q^{66} - 122786 q^{67} + 447632 q^{68} + 2458236 q^{69} - 676264 q^{70} - 267012 q^{71} - 1219564 q^{72} - 1322910 q^{73} - 661588 q^{74} - 400278 q^{75} + 873980 q^{76} - 2736932 q^{77} + 1480180 q^{78} - 1721864 q^{79} - 2377928 q^{80} + 3064239 q^{81} - 1407364 q^{82} + 5860478 q^{83} + 2103584 q^{84} + 3768888 q^{85} + 2146368 q^{86} - 2029892 q^{87} + 2855072 q^{88} - 3642238 q^{89} + 2497832 q^{90} - 7099204 q^{91} - 540888 q^{92} - 5896608 q^{93} - 2438936 q^{94} + 3127168 q^{96} + 4854926 q^{97} + 2073880 q^{98} + 11669854 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(32))$$

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
32.7.c $$\chi_{32}(31, \cdot)$$ 32.7.c.a 2 1
32.7.c.b 4
32.7.d $$\chi_{32}(15, \cdot)$$ 32.7.d.a 1 1
32.7.d.b 4
32.7.f $$\chi_{32}(7, \cdot)$$ None 0 2
32.7.h $$\chi_{32}(3, \cdot)$$ 32.7.h.a 92 4

## Decomposition of $$S_{7}^{\mathrm{old}}(\Gamma_1(32))$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(\Gamma_1(32)) \cong$$ $$S_{7}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$