Properties

Label 1900.1.j
Level $1900$
Weight $1$
Character orbit 1900.j
Rep. character $\chi_{1900}(607,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $2$
Sturm bound $300$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1900.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1900, [\chi])\).

Total New Old
Modular forms 40 24 16
Cusp forms 16 16 0
Eisenstein series 24 8 16

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

\( 16q + O(q^{10}) \) \( 16q - 16q^{26} - 16q^{36} + 16q^{66} - 16q^{81} + 16q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1900.1.j.a \(8\) \(0.948\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)
1900.1.j.b \(8\) \(0.948\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)