Properties

Label 3.9
Level 3
Weight 9
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(3))\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\(2q \) \(\mathstrut +\mathstrut 90q^{3} \) \(\mathstrut -\mathstrut 496q^{4} \) \(\mathstrut +\mathstrut 3024q^{6} \) \(\mathstrut -\mathstrut 3500q^{7} \) \(\mathstrut -\mathstrut 5022q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 90q^{3} \) \(\mathstrut -\mathstrut 496q^{4} \) \(\mathstrut +\mathstrut 3024q^{6} \) \(\mathstrut -\mathstrut 3500q^{7} \) \(\mathstrut -\mathstrut 5022q^{9} \) \(\mathstrut +\mathstrut 10080q^{10} \) \(\mathstrut -\mathstrut 22320q^{12} \) \(\mathstrut +\mathstrut 51460q^{13} \) \(\mathstrut -\mathstrut 30240q^{15} \) \(\mathstrut -\mathstrut 135040q^{16} \) \(\mathstrut +\mathstrut 272160q^{18} \) \(\mathstrut +\mathstrut 37876q^{19} \) \(\mathstrut -\mathstrut 157500q^{21} \) \(\mathstrut -\mathstrut 312480q^{22} \) \(\mathstrut +\mathstrut 24192q^{24} \) \(\mathstrut +\mathstrut 680450q^{25} \) \(\mathstrut -\mathstrut 1042470q^{27} \) \(\mathstrut +\mathstrut 868000q^{28} \) \(\mathstrut +\mathstrut 453600q^{30} \) \(\mathstrut -\mathstrut 702956q^{31} \) \(\mathstrut +\mathstrut 937440q^{33} \) \(\mathstrut -\mathstrut 3362688q^{34} \) \(\mathstrut +\mathstrut 1245456q^{36} \) \(\mathstrut +\mathstrut 2670340q^{37} \) \(\mathstrut +\mathstrut 2315700q^{39} \) \(\mathstrut +\mathstrut 80640q^{40} \) \(\mathstrut -\mathstrut 5292000q^{42} \) \(\mathstrut -\mathstrut 7052300q^{43} \) \(\mathstrut -\mathstrut 2721600q^{45} \) \(\mathstrut +\mathstrut 21123648q^{46} \) \(\mathstrut -\mathstrut 6076800q^{48} \) \(\mathstrut -\mathstrut 5404602q^{49} \) \(\mathstrut +\mathstrut 10088064q^{51} \) \(\mathstrut -\mathstrut 12762080q^{52} \) \(\mathstrut +\mathstrut 4653936q^{54} \) \(\mathstrut +\mathstrut 3124800q^{55} \) \(\mathstrut +\mathstrut 1704420q^{57} \) \(\mathstrut -\mathstrut 20694240q^{58} \) \(\mathstrut +\mathstrut 7499520q^{60} \) \(\mathstrut +\mathstrut 1507204q^{61} \) \(\mathstrut +\mathstrut 8788500q^{63} \) \(\mathstrut +\mathstrut 31425536q^{64} \) \(\mathstrut -\mathstrut 14061600q^{66} \) \(\mathstrut +\mathstrut 4537780q^{67} \) \(\mathstrut -\mathstrut 63370944q^{69} \) \(\mathstrut -\mathstrut 17640000q^{70} \) \(\mathstrut +\mathstrut 2177280q^{72} \) \(\mathstrut +\mathstrut 55345540q^{73} \) \(\mathstrut +\mathstrut 30620250q^{75} \) \(\mathstrut -\mathstrut 9393248q^{76} \) \(\mathstrut +\mathstrut 77807520q^{78} \) \(\mathstrut -\mathstrut 45961964q^{79} \) \(\mathstrut -\mathstrut 60872958q^{81} \) \(\mathstrut -\mathstrut 84208320q^{82} \) \(\mathstrut +\mathstrut 39060000q^{84} \) \(\mathstrut +\mathstrut 33626880q^{85} \) \(\mathstrut +\mathstrut 62082720q^{87} \) \(\mathstrut -\mathstrut 2499840q^{88} \) \(\mathstrut -\mathstrut 25310880q^{90} \) \(\mathstrut -\mathstrut 90055000q^{91} \) \(\mathstrut -\mathstrut 31633020q^{93} \) \(\mathstrut +\mathstrut 183238272q^{94} \) \(\mathstrut -\mathstrut 197987328q^{96} \) \(\mathstrut +\mathstrut 294542020q^{97} \) \(\mathstrut +\mathstrut 84369600q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.9.b \(\chi_{3}(2, \cdot)\) 3.9.b.a 2 1