# Properties

 Label 177.14 Level 177 Weight 14 Dimension 11246 Nonzero newspaces 4 Sturm bound 32480 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$177 = 3 \cdot 59$$ Weight: $$k$$ = $$14$$ Nonzero newspaces: $$4$$ Sturm bound: $$32480$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{14}(\Gamma_1(177))$$.

Total New Old
Modular forms 15196 11362 3834
Cusp forms 14964 11246 3718
Eisenstein series 232 116 116

## Trace form

 $$11246q + 132q^{2} - 1487q^{3} - 24994q^{4} - 21012q^{5} + 61207q^{6} - 428218q^{7} + 3661104q^{8} - 3188675q^{9} + O(q^{10})$$ $$11246q + 132q^{2} - 1487q^{3} - 24994q^{4} - 21012q^{5} + 61207q^{6} - 428218q^{7} + 3661104q^{8} - 3188675q^{9} - 7599586q^{10} + 21021000q^{11} - 41646341q^{12} - 51164494q^{13} + 249482784q^{14} - 103410137q^{15} - 150215770q^{16} + 67312116q^{17} + 70150183q^{18} - 84464386q^{19} - 831639408q^{20} + 373387939q^{21} + 2362841654q^{22} - 3380274960q^{23} + 3237214867q^{24} + 2679774380q^{25} - 5229401352q^{26} - 774841007q^{27} - 9013679098q^{28} + 11961751164q^{29} - 4482947621q^{30} - 353597866q^{31} + 19329359040q^{32} - 17285050757q^{33} - 3464285170q^{34} + 46416192000q^{35} - 13252012805q^{36} - 43826005438q^{37} - 45682094832q^{38} - 13826199449q^{39} + 62268351206q^{40} - 21160572828q^{41} + 173646750211q^{42} + 8398970894q^{43} - 333920969184q^{44} - 113997401892q^{45} + 381379090342q^{46} + 1134368153066q^{47} - 1436927267645q^{48} - 2346815482844q^{49} - 267519135556q^{50} + 1885030433811q^{51} + 3954478607766q^{52} + 437169253024q^{53} - 4696120399209q^{54} - 4701111676876q^{55} - 1736798035328q^{56} + 2559963926684q^{57} + 3697575028280q^{58} + 4205526809272q^{59} - 1730428094122q^{60} - 5013313751834q^{61} - 9339530959616q^{62} - 5194688747284q^{63} + 10806955660102q^{64} + 12103392660438q^{65} + 19798888967379q^{66} + 4254865940242q^{67} - 19970485757008q^{68} - 16744599638937q^{69} - 18060226833786q^{70} + 9267164822116q^{71} + 44790744771091q^{72} + 2474995548804q^{73} - 48390065360168q^{74} + 17083324897242q^{75} - 5766888774490q^{76} - 3695987708160q^{77} - 4093905678725q^{78} + 3572892259382q^{79} + 9411359483712q^{80} - 1694577218915q^{81} - 6239046035218q^{82} + 6900537556536q^{83} - 12088009681373q^{84} - 11174573203042q^{85} + 21648202598640q^{86} + 5068117469527q^{87} + 14865070169606q^{88} - 11011579222428q^{89} - 4038700759877q^{90} + 18596072577734q^{91} - 18419262671040q^{92} + 17702893407571q^{93} - 53394282181498q^{94} - 30330049072368q^{95} + 7210670010019q^{96} + 48180366643898q^{97} - 286826028671370q^{98} + 11171421260971q^{99} + O(q^{100})$$

## Decomposition of $$S_{14}^{\mathrm{new}}(\Gamma_1(177))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
177.14.a $$\chi_{177}(1, \cdot)$$ 177.14.a.a 30 1
177.14.a.b 31
177.14.a.c 31
177.14.a.d 32
177.14.d $$\chi_{177}(176, \cdot)$$ n/a 258 1
177.14.e $$\chi_{177}(4, \cdot)$$ n/a 3640 28
177.14.f $$\chi_{177}(2, \cdot)$$ n/a 7224 28

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{14}^{\mathrm{old}}(\Gamma_1(177))$$ into lower level spaces

$$S_{14}^{\mathrm{old}}(\Gamma_1(177)) \cong$$ $$S_{14}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 2}$$$$\oplus$$$$S_{14}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 2}$$