Properties

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

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
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

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

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