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Properties

Label 536.1.ba
Level $536$
Weight $1$
Character orbit 536.ba
Rep. character $\chi_{536}(19,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $68$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.ba (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 536 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(68\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(536, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8} + O(q^{10}) \) \( 20 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 2 q^{8} + 2 q^{11} - 12 q^{12} + q^{16} - 12 q^{17} - q^{19} - 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{27} + q^{32} - 2 q^{33} - q^{34} - q^{38} + 2 q^{41} + 2 q^{43} + 2 q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23 q^{54} + q^{57} - 9 q^{59} - 2 q^{64} - 18 q^{66} - 2 q^{67} + 2 q^{68} - q^{73} - 9 q^{75} + 2 q^{76} + 2 q^{81} + 18 q^{82} - 9 q^{83} - q^{86} + 2 q^{88} + 2 q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(536, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
536.1.ba.a 536.ba 536.aa $20$ $0.267$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-2}) \) None \(1\) \(2\) \(0\) \(0\) \(q-\zeta_{66}^{23}q^{2}+(\zeta_{66}^{14}-\zeta_{66}^{31})q^{3}+\cdots\)