Properties

Label 1156.1.c
Level $1156$
Weight $1$
Character orbit 1156.c
Rep. character $\chi_{1156}(579,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $153$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1156.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(153\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1156, [\chi])\).

Total New Old
Modular forms 21 18 3
Cusp forms 3 3 0
Eisenstein series 18 15 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{2} + 3 q^{4} - q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q - q^{2} + 3 q^{4} - q^{8} + 3 q^{9} - 2 q^{13} + 3 q^{16} - q^{18} + q^{25} - 2 q^{26} - q^{32} + 3 q^{36} + 3 q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} + 3 q^{64} - q^{72} + 3 q^{81} - 2 q^{89} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1156.1.c.a 1156.c 4.b $1$ $0.577$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{13}+q^{16}+\cdots\)
1156.1.c.b 1156.c 4.b $2$ $0.577$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots\)