↑

Properties

Label 10.12
Level 10
Weight 12
Dimension 11
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 72
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(10))\).

Total New Old
Modular forms 37 11 26
Cusp forms 29 11 18
Eisenstein series 8 0 8

Trace form

\( 11 q + 32 q^{2} + 1012 q^{3} - 1024 q^{4} + 3655 q^{5} + 2944 q^{6} - 45224 q^{7} + 32768 q^{8} - 159637 q^{9} + O(q^{10}) \) \( 11 q + 32 q^{2} + 1012 q^{3} - 1024 q^{4} + 3655 q^{5} + 2944 q^{6} - 45224 q^{7} + 32768 q^{8} - 159637 q^{9} - 285920 q^{10} + 29932 q^{11} + 1036288 q^{12} - 2191418 q^{13} - 4302592 q^{14} - 161180 q^{15} + 11534336 q^{16} + 12748506 q^{17} - 1427296 q^{18} - 53745980 q^{19} + 2657280 q^{20} + 101555152 q^{21} + 20705664 q^{22} - 98981928 q^{23} - 31850496 q^{24} - 132890725 q^{25} + 135891904 q^{26} + 423112600 q^{27} - 46309376 q^{28} - 550255470 q^{29} - 54314880 q^{30} + 112946752 q^{31} + 33554432 q^{32} + 134433024 q^{33} - 656797632 q^{34} - 556336360 q^{35} + 852384768 q^{36} + 403327246 q^{37} - 247560320 q^{38} + 2412868856 q^{39} + 497582080 q^{40} - 953091338 q^{41} - 1984111616 q^{42} - 1784459588 q^{43} + 1346957312 q^{44} + 2403558015 q^{45} - 2910183936 q^{46} - 1770523344 q^{47} + 1061158912 q^{48} + 7729962807 q^{49} + 4224762400 q^{50} - 11266516408 q^{51} - 2244012032 q^{52} + 219799902 q^{53} - 1802184960 q^{54} - 505693140 q^{55} - 51904512 q^{56} - 13068201520 q^{57} + 4214028480 q^{58} + 24462502060 q^{59} + 1265848320 q^{60} + 4035983482 q^{61} + 7243427584 q^{62} - 23253311128 q^{63} - 1073741824 q^{64} - 7992223130 q^{65} - 18111375872 q^{66} + 12541795636 q^{67} + 13054470144 q^{68} - 3407357504 q^{69} + 37412426240 q^{70} + 62154676392 q^{71} - 1461551104 q^{72} - 48488064638 q^{73} - 86491899712 q^{74} - 85616347900 q^{75} - 5660487680 q^{76} + 103920657552 q^{77} + 77720217088 q^{78} - 16354527920 q^{79} + 3832545280 q^{80} + 116916257331 q^{81} - 6817242816 q^{82} - 87174300588 q^{83} - 152972525568 q^{84} - 146862254310 q^{85} - 4125330816 q^{86} + 10614977880 q^{87} + 21202599936 q^{88} + 274708176590 q^{89} + 309751163040 q^{90} - 135806542768 q^{91} - 101357494272 q^{92} - 88457439856 q^{93} - 377363722752 q^{94} - 17026181900 q^{95} + 3087007744 q^{96} - 17065411814 q^{97} + 467353825056 q^{98} + 667711166156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.12.a \(\chi_{10}(1, \cdot)\) 10.12.a.a 1 1
10.12.a.b 1
10.12.a.c 1
10.12.a.d 2
10.12.b \(\chi_{10}(9, \cdot)\) 10.12.b.a 6 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)