↑

Properties

Label 82.2
Level 82
Weight 2
Dimension 69
Nonzero newspaces 6
Newform subspaces 14
Sturm bound 840
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 82 = 2 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 14 \)
Sturm bound: \(840\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(82))\).

Total New Old
Modular forms 250 69 181
Cusp forms 171 69 102
Eisenstein series 79 0 79

Trace form

\( 69 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 69 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} + 16 q^{30} + 8 q^{31} + 9 q^{32} + 72 q^{33} + 32 q^{34} + 32 q^{35} + 7 q^{36} + 82 q^{37} + 20 q^{38} + 104 q^{39} + 34 q^{40} - q^{41} + 128 q^{42} - 4 q^{43} + 28 q^{44} + 82 q^{45} + 16 q^{46} + 72 q^{47} + 16 q^{48} + 23 q^{49} + 19 q^{50} + 48 q^{51} - 4 q^{52} - 14 q^{53} - 72 q^{55} - 8 q^{56} - 80 q^{57} - 30 q^{58} - 60 q^{59} - 24 q^{60} - 62 q^{61} - 32 q^{62} - 104 q^{63} - q^{64} - 74 q^{65} - 48 q^{66} - 8 q^{67} - 18 q^{68} - 16 q^{69} - 48 q^{70} + 8 q^{71} - 13 q^{72} + 6 q^{73} - 38 q^{74} + 36 q^{75} - 20 q^{76} - 16 q^{77} - 56 q^{78} - 6 q^{80} + 49 q^{81} - 41 q^{82} - 4 q^{83} - 32 q^{84} + 62 q^{85} - 44 q^{86} - 40 q^{87} - 12 q^{88} - 10 q^{89} - 78 q^{90} + 48 q^{91} - 24 q^{92} - 48 q^{93} - 48 q^{94} - 40 q^{95} - 4 q^{96} - 18 q^{97} - 57 q^{98} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)

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
82.2.a \(\chi_{82}(1, \cdot)\) 82.2.a.a 1 1
82.2.a.b 2
82.2.b \(\chi_{82}(81, \cdot)\) 82.2.b.a 2 1
82.2.b.b 2
82.2.c \(\chi_{82}(9, \cdot)\) 82.2.c.a 2 2
82.2.c.b 2
82.2.c.c 2
82.2.d \(\chi_{82}(37, \cdot)\) 82.2.d.a 4 4
82.2.d.b 4
82.2.d.c 8
82.2.f \(\chi_{82}(23, \cdot)\) 82.2.f.a 8 4
82.2.f.b 8
82.2.g \(\chi_{82}(5, \cdot)\) 82.2.g.a 8 8
82.2.g.b 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(82))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(82)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)