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Properties

Label 756.2.cd
Level $756$
Weight $2$
Character orbit 756.cd
Rep. character $\chi_{756}(31,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $840$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.cd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 756 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

Trace form

\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} + O(q^{10}) \) \( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{10} - 9 q^{12} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 36 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} + 15 q^{30} - 63 q^{32} - 18 q^{33} - 18 q^{34} + 18 q^{36} - 12 q^{37} - 9 q^{38} - 9 q^{40} + 9 q^{42} - 6 q^{44} + 18 q^{45} - 6 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} + 57 q^{60} - 18 q^{61} + 99 q^{62} - 6 q^{64} - 54 q^{65} - 9 q^{66} - 54 q^{68} - 72 q^{69} + 9 q^{70} + 87 q^{72} - 69 q^{74} + 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} + 42 q^{81} - 18 q^{82} - 87 q^{84} + 6 q^{85} - 117 q^{86} + 21 q^{88} - 18 q^{89} - 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} + 54 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
756.2.cd.a 756.cd 756.bd $840$ $6.037$ None \(-3\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$