Properties

Label 12.4.b
Level $12$
Weight $4$
Character orbit 12.b
Rep. character $\chi_{12}(11,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)