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Properties

Label 3.9.b
Level $3$
Weight $9$
Character orbit 3.b
Rep. character $\chi_{3}(2,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(3, [\chi])\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(3, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.9.b.a \(2\) \(1.222\) \(\Q(\sqrt{-14}) \) None \(0\) \(90\) \(0\) \(-3500\) \(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)