Properties

Label 252.2.bj
Level $252$
Weight $2$
Character orbit 252.bj
Rep. character $\chi_{252}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 2q^{2} - 2q^{4} - 6q^{5} + 6q^{6} - 8q^{8} - 2q^{9} + O(q^{10}) \) \( 88q - 2q^{2} - 2q^{4} - 6q^{5} + 6q^{6} - 8q^{8} - 2q^{9} - 6q^{10} - 18q^{12} + 12q^{14} - 2q^{16} - 12q^{17} - 4q^{18} - 24q^{20} - 2q^{21} + 2q^{22} + 6q^{24} + 30q^{25} - 12q^{26} - 13q^{30} - 2q^{32} - 6q^{33} - 6q^{34} - 38q^{36} - 4q^{37} + 27q^{38} - 18q^{40} - 32q^{42} - 5q^{44} - 18q^{45} + 2q^{46} + 9q^{48} - 2q^{49} - 31q^{50} - 27q^{52} - 4q^{53} - 39q^{54} + 54q^{56} + 12q^{57} - 3q^{58} + 17q^{60} - 8q^{64} - 28q^{65} + 18q^{66} - 18q^{68} - 18q^{69} + 5q^{70} + 14q^{72} - 12q^{73} - 17q^{74} + 12q^{76} - 22q^{77} - 3q^{78} + 51q^{80} - 50q^{81} - 12q^{82} + 23q^{84} - 14q^{85} + 13q^{86} - 7q^{88} - 72q^{89} - 75q^{90} + 44q^{92} - 18q^{93} + 39q^{96} - 5q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.bj.a \(4\) \(2.012\) \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-12\) \(0\) \(q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
252.2.bj.b \(84\) \(2.012\) None \(2\) \(0\) \(6\) \(0\)