Properties

Label 12.4.b
Level 12
Weight 4
Character orbit b
Rep. character \(\chi_{12}(11,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(12, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 80q^{10} \) \(\mathstrut +\mathstrut 120q^{12} \) \(\mathstrut -\mathstrut 40q^{13} \) \(\mathstrut -\mathstrut 224q^{16} \) \(\mathstrut -\mathstrut 240q^{18} \) \(\mathstrut +\mathstrut 120q^{21} \) \(\mathstrut +\mathstrut 240q^{22} \) \(\mathstrut +\mathstrut 288q^{24} \) \(\mathstrut +\mathstrut 180q^{25} \) \(\mathstrut -\mathstrut 240q^{28} \) \(\mathstrut -\mathstrut 240q^{30} \) \(\mathstrut -\mathstrut 480q^{33} \) \(\mathstrut +\mathstrut 320q^{34} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 520q^{37} \) \(\mathstrut +\mathstrut 320q^{40} \) \(\mathstrut +\mathstrut 240q^{42} \) \(\mathstrut +\mathstrut 960q^{45} \) \(\mathstrut -\mathstrut 672q^{46} \) \(\mathstrut -\mathstrut 480q^{48} \) \(\mathstrut +\mathstrut 1132q^{49} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 792q^{54} \) \(\mathstrut -\mathstrut 1080q^{57} \) \(\mathstrut -\mathstrut 1360q^{58} \) \(\mathstrut -\mathstrut 960q^{60} \) \(\mathstrut -\mathstrut 1768q^{61} \) \(\mathstrut +\mathstrut 1408q^{64} \) \(\mathstrut +\mathstrut 1200q^{66} \) \(\mathstrut +\mathstrut 1344q^{69} \) \(\mathstrut +\mathstrut 480q^{70} \) \(\mathstrut -\mathstrut 960q^{72} \) \(\mathstrut +\mathstrut 1640q^{73} \) \(\mathstrut +\mathstrut 2160q^{76} \) \(\mathstrut +\mathstrut 240q^{78} \) \(\mathstrut -\mathstrut 2844q^{81} \) \(\mathstrut -\mathstrut 1120q^{82} \) \(\mathstrut -\mathstrut 240q^{84} \) \(\mathstrut -\mathstrut 1280q^{85} \) \(\mathstrut -\mathstrut 2880q^{88} \) \(\mathstrut -\mathstrut 240q^{90} \) \(\mathstrut +\mathstrut 3480q^{93} \) \(\mathstrut -\mathstrut 1344q^{94} \) \(\mathstrut +\mathstrut 384q^{96} \) \(\mathstrut +\mathstrut 3080q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.4.b.a \(4\) \(0.708\) \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)