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Properties

Label 440.1.bh
Level $440$
Weight $1$
Character orbit 440.bh
Rep. character $\chi_{440}(59,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $2$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 440.bh (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(440, [\chi])\).

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

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

\( 8 q - 2 q^{4} - 2 q^{9} + 8 q^{10} - 2 q^{11} + 6 q^{14} - 2 q^{16} - 4 q^{19} - 2 q^{25} - 4 q^{26} - 4 q^{35} - 2 q^{36} - 2 q^{40} + 6 q^{41} - 2 q^{44} - 4 q^{46} + 4 q^{49} - 4 q^{56} - 4 q^{59} - 2 q^{64}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.1.bh.a 440.bh 440.ah $4$ $0.220$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-10}) \) None 440.1.bh.a \(-1\) \(0\) \(-1\) \(3\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
440.1.bh.b 440.bh 440.ah $4$ $0.220$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-10}) \) None 440.1.bh.a \(1\) \(0\) \(1\) \(-3\) \(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)