Properties

Label 1840.1.bq
Level $1840$
Weight $1$
Character orbit 1840.bq
Rep. character $\chi_{1840}(239,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $20$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1840.bq (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1840, [\chi])\).

Total New Old
Modular forms 200 20 180
Cusp forms 80 20 60
Eisenstein series 120 0 120

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q + 2q^{5} + 2q^{9} + O(q^{10}) \) \( 20q + 2q^{5} + 2q^{9} - 2q^{25} - 4q^{29} + 4q^{41} - 24q^{45} - 20q^{49} + 4q^{61} - 2q^{81} - 4q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1840.1.bq.a \(20\) \(0.918\) \(\Q(\zeta_{44})\) \(D_{22}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{44}^{7}-\zeta_{44}^{9})q^{3}+\zeta_{44}^{6}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)