Properties

Label 100.1.j
Level 100
Weight 1
Character orbit j
Rep. character \(\chi_{100}(11,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
Newform subspaces 1
Sturm bound 15
Trace bound 0

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 100.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(100, [\chi])\).

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

\( 4q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} + O(q^{10}) \) \( 4q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} - q^{10} - 2q^{13} - q^{16} - 2q^{17} + 4q^{18} + 4q^{20} - q^{25} - 2q^{26} - 2q^{29} + 4q^{32} + 3q^{34} - q^{36} + 3q^{37} - q^{40} - 2q^{41} - q^{45} + 4q^{49} - q^{50} - 2q^{52} + 3q^{53} - 2q^{58} - 2q^{61} - q^{64} + 3q^{65} - 2q^{68} - q^{72} - 2q^{73} - 2q^{74} - q^{80} - q^{81} - 2q^{82} + 3q^{85} + 3q^{89} - q^{90} - 2q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.1.j.a \(4\) \(0.050\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)