↑

Properties

Label 30.11
Level 30
Weight 11
Dimension 52
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 528
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(528\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(30))\).

Total New Old
Modular forms 256 52 204
Cusp forms 224 52 172
Eisenstein series 32 0 32

Trace form

\( 52 q + 64 q^{2} - 44 q^{3} + 4096 q^{4} - 15120 q^{5} + 1408 q^{6} + 69016 q^{7} - 32768 q^{8} - 200224 q^{9} + O(q^{10}) \) \( 52 q + 64 q^{2} - 44 q^{3} + 4096 q^{4} - 15120 q^{5} + 1408 q^{6} + 69016 q^{7} - 32768 q^{8} - 200224 q^{9} + 68928 q^{10} - 32080 q^{11} + 22528 q^{12} - 210588 q^{13} + 2108524 q^{15} + 3145728 q^{16} - 4770676 q^{17} + 3112640 q^{18} + 1205856 q^{19} - 1595392 q^{20} - 10940096 q^{21} - 387584 q^{22} + 29499344 q^{23} + 5505024 q^{24} - 80870324 q^{25} - 31831680 q^{26} - 71000468 q^{27} - 35336192 q^{28} + 73459200 q^{30} - 26204384 q^{31} - 16777216 q^{32} - 61135992 q^{33} - 115563008 q^{34} - 46334992 q^{35} + 237139968 q^{36} + 275377980 q^{37} + 35204096 q^{38} + 142407320 q^{39} - 19759104 q^{40} + 226717760 q^{41} - 289912064 q^{42} - 637256568 q^{43} + 283420020 q^{45} + 887043328 q^{46} - 129179424 q^{47} - 11534336 q^{48} - 1709721960 q^{49} + 817307072 q^{50} - 564203704 q^{51} + 896231424 q^{52} + 1416549700 q^{53} + 944021760 q^{54} - 802893296 q^{55} - 418119680 q^{56} - 1786867384 q^{57} - 566358016 q^{58} + 1360939008 q^{60} + 3418160368 q^{61} + 4455320320 q^{62} + 3371340848 q^{63} + 1073741824 q^{64} - 7724537484 q^{65} - 6382032896 q^{66} - 1182228728 q^{67} + 2442586112 q^{68} - 1796087576 q^{69} + 2878447872 q^{70} + 3325553920 q^{71} - 303726592 q^{72} - 4242562708 q^{73} + 1085735516 q^{75} - 4703076352 q^{76} - 2118642848 q^{77} - 1619525504 q^{78} + 10028832864 q^{79} + 3963617280 q^{80} - 7156707396 q^{81} - 3701680640 q^{82} - 5613456768 q^{83} + 3448123392 q^{84} - 7787801404 q^{85} - 15912491520 q^{86} - 6337925088 q^{87} + 198443008 q^{88} - 1085866944 q^{90} + 12658705680 q^{91} + 15103664128 q^{92} - 11551584448 q^{93} + 4503772160 q^{94} + 50807490304 q^{95} + 369098752 q^{96} - 15093074004 q^{97} - 49552897984 q^{98} - 68158894576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(30))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
30.11.b \(\chi_{30}(29, \cdot)\) 30.11.b.a 20 1
30.11.d \(\chi_{30}(11, \cdot)\) 30.11.d.a 12 1
30.11.f \(\chi_{30}(7, \cdot)\) 30.11.f.a 8 2
30.11.f.b 12

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)