Properties

Label 538.2.e
Level $538$
Weight $2$
Character orbit 538.e
Rep. character $\chi_{538}(9,\cdot)$
Character field $\Q(\zeta_{134})$
Dimension $1452$
Newform subspaces $1$
Sturm bound $135$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 538 = 2 \cdot 269 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 538.e (of order \(134\) and degree \(66\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 269 \)
Character field: \(\Q(\zeta_{134})\)
Newform subspaces: \( 1 \)
Sturm bound: \(135\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(538, [\chi])\).

Total New Old
Modular forms 4620 1452 3168
Cusp forms 4356 1452 2904
Eisenstein series 264 0 264

Trace form

\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + O(q^{10}) \) \( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(538, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
538.2.e.a 538.e 269.e $1452$ $4.296$ None 538.2.e.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{134}]$

Decomposition of \(S_{2}^{\mathrm{old}}(538, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(538, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(269, [\chi])\)\(^{\oplus 2}\)