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Properties

Label 1099.1.b
Level $1099$
Weight $1$
Character orbit 1099.b
Rep. character $\chi_{1099}(1098,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $105$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1099 = 7 \cdot 157 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1099.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1099 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(105\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1099, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 0

Trace form

\( 6 q - 2 q^{4} - 2 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{4} - 2 q^{9} - 6 q^{11} - 2 q^{16} - 8 q^{30} + 2 q^{35} + 6 q^{36} - 6 q^{37} + 8 q^{39} - 8 q^{42} + 2 q^{44} - 8 q^{46} + 6 q^{49} + 8 q^{51} - 8 q^{57} + 6 q^{64} + 2 q^{67} - 6 q^{71} - 2 q^{81} + 8 q^{86} + 8 q^{93} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1099, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1099.1.b.a 1099.b 1099.b $1$ $0.548$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1099}) \) None \(0\) \(0\) \(-1\) \(1\) \(q+q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+q^{16}+\cdots\)
1099.1.b.b 1099.b 1099.b $1$ $0.548$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1099}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+q^{16}+\cdots\)
1099.1.b.c 1099.b 1099.b $2$ $0.548$ \(\Q(\sqrt{-2}) \) $S_{4}$ None None \(0\) \(0\) \(-2\) \(-2\) \(q+\beta q^{2}-\beta q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
1099.1.b.d 1099.b 1099.b $2$ $0.548$ \(\Q(\sqrt{-2}) \) $S_{4}$ None None \(0\) \(0\) \(2\) \(2\) \(q-\beta q^{2}-\beta q^{3}-q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)