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Properties

Label 102.2
Level 102
Weight 2
Dimension 73
Nonzero newspaces 5
Newforms 9
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newforms: \( 9 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(102))\).

Total New Old
Modular forms 352 73 279
Cusp forms 225 73 152
Eisenstein series 127 0 127

Trace form

\(73q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(73q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 20q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 24q^{14} \) \(\mathstrut -\mathstrut 42q^{15} \) \(\mathstrut -\mathstrut 7q^{16} \) \(\mathstrut -\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 31q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 40q^{21} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut -\mathstrut 41q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut -\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 56q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 62q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 48q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 57q^{49} \) \(\mathstrut +\mathstrut 31q^{50} \) \(\mathstrut +\mathstrut 81q^{51} \) \(\mathstrut +\mathstrut 14q^{52} \) \(\mathstrut +\mathstrut 46q^{53} \) \(\mathstrut +\mathstrut 57q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 92q^{57} \) \(\mathstrut +\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 38q^{60} \) \(\mathstrut +\mathstrut 30q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 76q^{65} \) \(\mathstrut +\mathstrut 20q^{66} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut +\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut -\mathstrut 94q^{73} \) \(\mathstrut -\mathstrut 34q^{74} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 64q^{77} \) \(\mathstrut -\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut -\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 98q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 18q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut -\mathstrut 80q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)

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
102.2.a \(\chi_{102}(1, \cdot)\) 102.2.a.a 1 1
102.2.a.b 1
102.2.a.c 1
102.2.b \(\chi_{102}(67, \cdot)\) 102.2.b.a 2 1
102.2.f \(\chi_{102}(13, \cdot)\) 102.2.f.a 4 2
102.2.h \(\chi_{102}(19, \cdot)\) 102.2.h.a 8 4
102.2.h.b 8
102.2.i \(\chi_{102}(5, \cdot)\) 102.2.i.a 24 8
102.2.i.b 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)