Properties

Label 12.3.d
Level $12$
Weight $3$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.3.d.a 12.d 4.b $2$ $0.327$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)