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

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

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

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 \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)