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Properties

Label 588.2.u
Level $588$
Weight $2$
Character orbit 588.u
Rep. character $\chi_{588}(71,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $648$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.u (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

Total New Old
Modular forms 696 696 0
Cusp forms 648 648 0
Eisenstein series 48 48 0

Trace form

\( 648 q - 10 q^{4} - q^{6} - 10 q^{9} + O(q^{10}) \) \( 648 q - 10 q^{4} - q^{6} - 10 q^{9} - 18 q^{10} - 36 q^{12} - 28 q^{13} - 10 q^{16} - 6 q^{18} - 14 q^{21} + 10 q^{22} - 9 q^{24} + 80 q^{25} - 64 q^{28} - 24 q^{30} + 2 q^{33} + 10 q^{34} + 23 q^{36} - 40 q^{37} - 90 q^{40} - 17 q^{42} - 38 q^{45} - 22 q^{46} - 60 q^{48} - 16 q^{49} + 14 q^{52} - 17 q^{54} + 20 q^{57} - 2 q^{58} + 53 q^{60} - 40 q^{61} - 46 q^{64} - 23 q^{66} - 46 q^{69} - 72 q^{70} + q^{72} - 52 q^{73} - 66 q^{76} + 29 q^{78} + 90 q^{81} - 92 q^{82} - 70 q^{84} - 60 q^{85} + 46 q^{88} - 25 q^{90} + 4 q^{93} + 70 q^{94} + 34 q^{96} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.2.u.a 588.u 588.u $648$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$