Properties

 Label 20.10 Level 20 Weight 10 Dimension 57 Nonzero newspaces 3 Newforms 5 Sturm bound 240 Trace bound 1

Defining parameters

 Level: $$N$$ = $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$3$$ Newforms: $$5$$ Sturm bound: $$240$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(20))$$.

Total New Old
Modular forms 118 65 53
Cusp forms 98 57 41
Eisenstein series 20 8 12

Trace form

 $$57q$$ $$\mathstrut -\mathstrut 2q^{2}$$ $$\mathstrut -\mathstrut 308q^{3}$$ $$\mathstrut +\mathstrut 31q^{5}$$ $$\mathstrut +\mathstrut 6152q^{6}$$ $$\mathstrut -\mathstrut 912q^{7}$$ $$\mathstrut -\mathstrut 716q^{8}$$ $$\mathstrut +\mathstrut 8459q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$57q$$ $$\mathstrut -\mathstrut 2q^{2}$$ $$\mathstrut -\mathstrut 308q^{3}$$ $$\mathstrut +\mathstrut 31q^{5}$$ $$\mathstrut +\mathstrut 6152q^{6}$$ $$\mathstrut -\mathstrut 912q^{7}$$ $$\mathstrut -\mathstrut 716q^{8}$$ $$\mathstrut +\mathstrut 8459q^{9}$$ $$\mathstrut +\mathstrut 11446q^{10}$$ $$\mathstrut +\mathstrut 34740q^{11}$$ $$\mathstrut -\mathstrut 155360q^{12}$$ $$\mathstrut -\mathstrut 6704q^{13}$$ $$\mathstrut +\mathstrut 32740q^{15}$$ $$\mathstrut +\mathstrut 3000q^{16}$$ $$\mathstrut -\mathstrut 637428q^{17}$$ $$\mathstrut -\mathstrut 679086q^{18}$$ $$\mathstrut -\mathstrut 447636q^{19}$$ $$\mathstrut -\mathstrut 334324q^{20}$$ $$\mathstrut +\mathstrut 1944376q^{21}$$ $$\mathstrut +\mathstrut 3176920q^{22}$$ $$\mathstrut -\mathstrut 808416q^{23}$$ $$\mathstrut +\mathstrut 5274381q^{25}$$ $$\mathstrut -\mathstrut 11222732q^{26}$$ $$\mathstrut -\mathstrut 8154584q^{27}$$ $$\mathstrut +\mathstrut 12731840q^{28}$$ $$\mathstrut +\mathstrut 899874q^{29}$$ $$\mathstrut +\mathstrut 15498680q^{30}$$ $$\mathstrut +\mathstrut 7989712q^{31}$$ $$\mathstrut -\mathstrut 29092792q^{32}$$ $$\mathstrut -\mathstrut 13035520q^{33}$$ $$\mathstrut -\mathstrut 8209160q^{35}$$ $$\mathstrut +\mathstrut 44773372q^{36}$$ $$\mathstrut +\mathstrut 6991724q^{37}$$ $$\mathstrut -\mathstrut 26115120q^{38}$$ $$\mathstrut +\mathstrut 27695864q^{39}$$ $$\mathstrut -\mathstrut 55995604q^{40}$$ $$\mathstrut +\mathstrut 552302q^{41}$$ $$\mathstrut +\mathstrut 82830200q^{42}$$ $$\mathstrut -\mathstrut 32882700q^{43}$$ $$\mathstrut -\mathstrut 54538499q^{45}$$ $$\mathstrut -\mathstrut 92534488q^{46}$$ $$\mathstrut +\mathstrut 78552936q^{47}$$ $$\mathstrut +\mathstrut 46448320q^{48}$$ $$\mathstrut +\mathstrut 216766143q^{49}$$ $$\mathstrut -\mathstrut 54429014q^{50}$$ $$\mathstrut -\mathstrut 114424456q^{51}$$ $$\mathstrut +\mathstrut 88926156q^{52}$$ $$\mathstrut -\mathstrut 274039236q^{53}$$ $$\mathstrut -\mathstrut 282892300q^{55}$$ $$\mathstrut -\mathstrut 177356448q^{56}$$ $$\mathstrut +\mathstrut 270379472q^{57}$$ $$\mathstrut +\mathstrut 82723048q^{58}$$ $$\mathstrut +\mathstrut 466689828q^{59}$$ $$\mathstrut +\mathstrut 166923520q^{60}$$ $$\mathstrut +\mathstrut 366448194q^{61}$$ $$\mathstrut -\mathstrut 292810200q^{62}$$ $$\mathstrut -\mathstrut 723019072q^{63}$$ $$\mathstrut -\mathstrut 526945428q^{65}$$ $$\mathstrut +\mathstrut 614341200q^{66}$$ $$\mathstrut -\mathstrut 26145732q^{67}$$ $$\mathstrut -\mathstrut 289868412q^{68}$$ $$\mathstrut +\mathstrut 1021502632q^{69}$$ $$\mathstrut -\mathstrut 203227600q^{70}$$ $$\mathstrut +\mathstrut 224888616q^{71}$$ $$\mathstrut +\mathstrut 930217668q^{72}$$ $$\mathstrut -\mathstrut 44807784q^{73}$$ $$\mathstrut -\mathstrut 1158654100q^{75}$$ $$\mathstrut -\mathstrut 1061841600q^{76}$$ $$\mathstrut -\mathstrut 195453840q^{77}$$ $$\mathstrut +\mathstrut 49362600q^{78}$$ $$\mathstrut +\mathstrut 2245791312q^{79}$$ $$\mathstrut +\mathstrut 210150736q^{80}$$ $$\mathstrut -\mathstrut 552782283q^{81}$$ $$\mathstrut -\mathstrut 591442904q^{82}$$ $$\mathstrut -\mathstrut 1909553076q^{83}$$ $$\mathstrut -\mathstrut 538201268q^{85}$$ $$\mathstrut -\mathstrut 874588728q^{86}$$ $$\mathstrut +\mathstrut 585010632q^{87}$$ $$\mathstrut +\mathstrut 865939360q^{88}$$ $$\mathstrut +\mathstrut 1748967126q^{89}$$ $$\mathstrut +\mathstrut 1779829206q^{90}$$ $$\mathstrut +\mathstrut 781823568q^{91}$$ $$\mathstrut -\mathstrut 1106673600q^{92}$$ $$\mathstrut -\mathstrut 4005699248q^{93}$$ $$\mathstrut -\mathstrut 2253979460q^{95}$$ $$\mathstrut +\mathstrut 1870685312q^{96}$$ $$\mathstrut +\mathstrut 5101092544q^{97}$$ $$\mathstrut -\mathstrut 3885590026q^{98}$$ $$\mathstrut +\mathstrut 4822342340q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(20))$$

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
20.10.a $$\chi_{20}(1, \cdot)$$ 20.10.a.a 1 1
20.10.a.b 2
20.10.c $$\chi_{20}(9, \cdot)$$ 20.10.c.a 4 1
20.10.e $$\chi_{20}(3, \cdot)$$ 20.10.e.a 2 2
20.10.e.b 48

Decomposition of $$S_{10}^{\mathrm{old}}(\Gamma_1(20))$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(\Gamma_1(20)) \cong$$ $$S_{10}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 2}$$