Properties

Label 12.3.d
Level 12
Weight 3
Character orbit d
Rep. character \(\chi_{12}(7,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 24q^{14} \) \(\mathstrut -\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 20q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 52q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 20q^{34} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut +\mathstrut 72q^{38} \) \(\mathstrut -\mathstrut 32q^{40} \) \(\mathstrut +\mathstrut 116q^{41} \) \(\mathstrut -\mathstrut 24q^{42} \) \(\mathstrut -\mathstrut 48q^{44} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 48q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 148q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut +\mathstrut 52q^{58} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 52q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 128q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 40q^{68} \) \(\mathstrut +\mathstrut 96q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut -\mathstrut 92q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 144q^{76} \) \(\mathstrut +\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 32q^{80} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 116q^{82} \) \(\mathstrut -\mathstrut 48q^{84} \) \(\mathstrut -\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 168q^{86} \) \(\mathstrut +\mathstrut 164q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 192q^{92} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 240q^{94} \) \(\mathstrut -\mathstrut 96q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.3.d.a \(2\) \(0.327\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)