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Properties

Label 3536.1.bh
Level $3536$
Weight $1$
Character orbit 3536.bh
Rep. character $\chi_{3536}(1461,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $504$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3536 = 2^{4} \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3536.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3536 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(504\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3536, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{2} + 2 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} + 2 q^{8} + 2 q^{13} + 4 q^{16} - 2 q^{18} + 4 q^{25} + 2 q^{32} + 2 q^{34} + 4 q^{43} - 4 q^{47} + 2 q^{50} - 2 q^{52} + 2 q^{72} - 4 q^{81} - 4 q^{94} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3536, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3536.1.bh.a 3536.bh 3536.ah $2$ $1.765$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{17}) \) 3536.1.bh.a \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{13}+\cdots\)
3536.1.bh.b 3536.bh 3536.ah $2$ $1.765$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{17}) \) 3536.1.bh.b \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+iq^{9}-iq^{13}+q^{16}+\cdots\)