Properties

Label 83.7
Level 83
Weight 7
Dimension 1681
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 4018
Trace bound 1

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Defining parameters

Level: \( N \) = \( 83 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(4018\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(83))\).

Total New Old
Modular forms 1763 1763 0
Cusp forms 1681 1681 0
Eisenstein series 82 82 0

Trace form

\( 1681 q - 41 q^{2} - 41 q^{3} - 41 q^{4} - 41 q^{5} - 41 q^{6} - 41 q^{7} - 41 q^{8} - 41 q^{9} + O(q^{10}) \) \( 1681 q - 41 q^{2} - 41 q^{3} - 41 q^{4} - 41 q^{5} - 41 q^{6} - 41 q^{7} - 41 q^{8} - 41 q^{9} - 41 q^{10} - 41 q^{11} - 41 q^{12} - 41 q^{13} - 41 q^{14} - 41 q^{15} - 41 q^{16} - 41 q^{17} - 41 q^{18} - 41 q^{19} - 41 q^{20} - 41 q^{21} - 41 q^{22} - 41 q^{23} - 41 q^{24} - 41 q^{25} - 41 q^{26} - 41 q^{27} - 41 q^{28} - 41 q^{29} - 41 q^{30} - 41 q^{31} - 41 q^{32} - 41 q^{33} - 41 q^{34} - 41 q^{35} - 41 q^{36} - 41 q^{37} - 41 q^{38} - 41 q^{39} - 41 q^{40} - 41 q^{41} - 41 q^{42} - 41 q^{43} - 41 q^{44} - 41 q^{45} - 41 q^{46} - 41 q^{47} - 41 q^{48} - 41 q^{49} - 41 q^{50} - 41 q^{51} - 41 q^{52} - 41 q^{53} - 41 q^{54} - 41 q^{55} - 41 q^{56} - 41 q^{57} - 41 q^{58} - 41 q^{59} - 41 q^{60} - 41 q^{61} - 41 q^{62} - 41 q^{63} - 41 q^{64} - 41 q^{65} + 7229079 q^{66} + 2332039 q^{67} - 2351145 q^{68} - 6076241 q^{69} - 9611753 q^{70} - 2074641 q^{71} - 13316841 q^{72} - 1222169 q^{73} + 1036439 q^{74} + 9193143 q^{75} + 7557079 q^{76} + 6587839 q^{77} + 22166199 q^{78} + 5889199 q^{79} + 14707479 q^{80} + 3174999 q^{81} - 2501369 q^{83} - 19522642 q^{84} - 6898865 q^{85} - 11112681 q^{86} - 11998281 q^{87} - 29165801 q^{88} - 7507961 q^{89} - 17567721 q^{90} - 2125481 q^{91} + 2309079 q^{92} + 13966527 q^{93} + 6789559 q^{94} + 13725775 q^{95} + 52807959 q^{96} + 5195479 q^{97} + 15754455 q^{98} + 3178279 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(83))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
83.7.b \(\chi_{83}(82, \cdot)\) 83.7.b.a 1 1
83.7.b.b 2
83.7.b.c 38
83.7.d \(\chi_{83}(2, \cdot)\) 83.7.d.a 1640 40