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Properties

Label 693.2.cj
Level $693$
Weight $2$
Character orbit 693.cj
Rep. character $\chi_{693}(20,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $736$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.cj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

Total New Old
Modular forms 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

Trace form

\( 736 q - 18 q^{2} - 94 q^{4} - 3 q^{7} - 24 q^{9} + O(q^{10}) \) \( 736 q - 18 q^{2} - 94 q^{4} - 3 q^{7} - 24 q^{9} - 30 q^{11} - 9 q^{14} - 18 q^{15} + 66 q^{16} - 20 q^{18} - 84 q^{23} + 70 q^{25} - 20 q^{28} - 18 q^{29} + 12 q^{30} - 96 q^{32} - 44 q^{36} - 24 q^{37} - 84 q^{39} - 27 q^{42} - 16 q^{43} - 48 q^{46} - 3 q^{49} + 168 q^{50} + 16 q^{51} - 138 q^{56} + 32 q^{57} + 46 q^{58} + 2 q^{60} - 53 q^{63} + 48 q^{64} - 60 q^{65} - 16 q^{67} - 18 q^{70} - 200 q^{72} + 6 q^{74} - 111 q^{77} + 136 q^{78} + 6 q^{79} - 104 q^{81} - 63 q^{84} + 2 q^{85} - 42 q^{86} - 44 q^{88} + 16 q^{91} + 282 q^{92} - 74 q^{93} - 150 q^{95} + 164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
693.2.cj.a 693.cj 693.bj $736$ $5.534$ None \(-18\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{30}]$