Properties

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

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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

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

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 the 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

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