Properties

Label 1900.1.bb
Level $1900$
Weight $1$
Character orbit 1900.bb
Rep. character $\chi_{1900}(341,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $1$
Sturm bound $300$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1900.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(300\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + q^{5} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( 8q + q^{5} + 2q^{7} - 2q^{9} - 3q^{11} - 3q^{17} - 2q^{19} + 6q^{23} + q^{25} - 6q^{35} + 2q^{43} + q^{45} + 2q^{47} + 10q^{49} - q^{55} + 2q^{61} - 3q^{63} + 2q^{73} - 2q^{77} - 2q^{81} + 6q^{83} - 6q^{85} + q^{95} + 2q^{99} + O(q^{100}) \)

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.bb.a \(8\) \(0.948\) \(\Q(\zeta_{15})\) \(D_{15}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(2\) \(q-\zeta_{30}^{7}q^{5}+(\zeta_{30}^{2}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{12}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)