# Properties

 Label 176.4 Level 176 Weight 4 Dimension 1553 Nonzero newspaces 8 Newform subspaces 27 Sturm bound 7680 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Newform subspaces: $$27$$ Sturm bound: $$7680$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(176))$$.

Total New Old
Modular forms 3020 1633 1387
Cusp forms 2740 1553 1187
Eisenstein series 280 80 200

## Trace form

 $$1553 q - 16 q^{2} - 19 q^{3} - 36 q^{4} - 17 q^{5} + 44 q^{6} + 33 q^{7} + 68 q^{8} + 17 q^{9} + O(q^{10})$$ $$1553 q - 16 q^{2} - 19 q^{3} - 36 q^{4} - 17 q^{5} + 44 q^{6} + 33 q^{7} + 68 q^{8} + 17 q^{9} + 116 q^{10} - 77 q^{11} - 240 q^{12} - 65 q^{13} - 396 q^{14} + 249 q^{15} - 580 q^{16} - 137 q^{17} - 368 q^{18} + 125 q^{19} + 372 q^{20} + 58 q^{21} + 568 q^{22} - 142 q^{23} + 1676 q^{24} + 237 q^{25} + 508 q^{26} - 79 q^{27} - 580 q^{28} - 17 q^{29} - 2492 q^{30} - 1071 q^{31} - 1956 q^{32} - 1557 q^{33} - 912 q^{34} - 1933 q^{35} + 1172 q^{36} + 339 q^{37} + 2444 q^{38} + 1189 q^{39} + 2652 q^{40} + 1871 q^{41} + 1340 q^{42} + 3060 q^{43} - 888 q^{44} + 1978 q^{45} - 2284 q^{46} + 3859 q^{47} - 3556 q^{48} - 179 q^{49} - 1472 q^{50} + 1805 q^{51} + 452 q^{52} + 275 q^{53} + 2732 q^{54} - 2597 q^{55} + 936 q^{56} - 2433 q^{57} - 36 q^{58} - 4763 q^{59} + 364 q^{60} - 2945 q^{61} + 140 q^{62} - 5664 q^{63} - 1044 q^{64} + 1022 q^{65} + 408 q^{66} - 3538 q^{67} + 1740 q^{68} - 1768 q^{69} + 6520 q^{70} + 3291 q^{71} + 13096 q^{72} + 9527 q^{73} + 10384 q^{74} + 9621 q^{75} + 9636 q^{76} + 3139 q^{77} + 2224 q^{78} + 6755 q^{79} - 1544 q^{80} - 5787 q^{81} - 10012 q^{82} + 2231 q^{83} - 21940 q^{84} - 12761 q^{85} - 21148 q^{86} - 6794 q^{87} - 29388 q^{88} - 8238 q^{89} - 29732 q^{90} - 10123 q^{91} - 12004 q^{92} - 6041 q^{93} - 4324 q^{94} - 15541 q^{95} + 5844 q^{96} + 1279 q^{97} + 4412 q^{98} - 2239 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$

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
176.4.a $$\chi_{176}(1, \cdot)$$ 176.4.a.a 1 1
176.4.a.b 1
176.4.a.c 1
176.4.a.d 1
176.4.a.e 1
176.4.a.f 1
176.4.a.g 2
176.4.a.h 2
176.4.a.i 2
176.4.a.j 3
176.4.c $$\chi_{176}(89, \cdot)$$ None 0 1
176.4.e $$\chi_{176}(175, \cdot)$$ 176.4.e.a 2 1
176.4.e.b 2
176.4.e.c 2
176.4.e.d 4
176.4.e.e 8
176.4.g $$\chi_{176}(87, \cdot)$$ None 0 1
176.4.i $$\chi_{176}(43, \cdot)$$ 176.4.i.a 140 2
176.4.j $$\chi_{176}(45, \cdot)$$ 176.4.j.a 120 2
176.4.m $$\chi_{176}(49, \cdot)$$ 176.4.m.a 4 4
176.4.m.b 8
176.4.m.c 8
176.4.m.d 12
176.4.m.e 16
176.4.m.f 20
176.4.o $$\chi_{176}(7, \cdot)$$ None 0 4
176.4.q $$\chi_{176}(63, \cdot)$$ 176.4.q.a 24 4
176.4.q.b 48
176.4.s $$\chi_{176}(9, \cdot)$$ None 0 4
176.4.w $$\chi_{176}(5, \cdot)$$ 176.4.w.a 560 8
176.4.x $$\chi_{176}(19, \cdot)$$ 176.4.x.a 560 8

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(176))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(176)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 1}$$