Properties

Label 588.2.x
Level $588$
Weight $2$
Character orbit 588.x
Rep. character $\chi_{588}(55,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Newform subspaces $2$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.x (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 696 336 360
Cusp forms 648 336 312
Eisenstein series 48 0 48

Trace form

\( 336 q + 12 q^{8} - 56 q^{9} + O(q^{10}) \) \( 336 q + 12 q^{8} - 56 q^{9} + 2 q^{14} + 16 q^{16} + 4 q^{21} - 12 q^{22} - 42 q^{24} + 64 q^{25} - 60 q^{28} - 16 q^{30} - 20 q^{32} - 112 q^{34} - 20 q^{37} + 56 q^{40} + 16 q^{42} + 40 q^{44} - 16 q^{49} + 228 q^{50} - 16 q^{53} + 22 q^{56} + 24 q^{57} - 12 q^{58} + 20 q^{60} - 28 q^{61} - 16 q^{65} + 78 q^{70} - 30 q^{72} + 44 q^{74} - 42 q^{76} + 16 q^{77} + 12 q^{78} - 56 q^{81} - 16 q^{84} - 48 q^{85} - 40 q^{86} - 148 q^{88} + 14 q^{92} - 8 q^{93} - 42 q^{94} - 268 q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.2.x.a $168$ $4.695$ None \(0\) \(-28\) \(0\) \(2\)
588.2.x.b $168$ $4.695$ None \(0\) \(28\) \(0\) \(-2\)

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)