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Properties

Label 1155.1.ca
Level $1155$
Weight $1$
Character orbit 1155.ca
Rep. character $\chi_{1155}(314,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $2$
Sturm bound $192$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1155.ca (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1155 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1155, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 4 q^{4} - 6 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{4} - 6 q^{9} - 6 q^{15} - 4 q^{16} + 4 q^{25} + 4 q^{36} - 10 q^{39} + 4 q^{49} - 10 q^{51} + 4 q^{60} - 4 q^{64} + 6 q^{81} + 10 q^{84} + 12 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1155.1.ca.a 1155.ca 1155.ba $8$ $0.576$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
1155.1.ca.b 1155.ca 1155.ba $8$ $0.576$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)