Properties

Label 320.1.h
Level $320$
Weight $1$
Character orbit 320.h
Rep. character $\chi_{320}(319,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 320.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(320, [\chi])\).

Total New Old
Modular forms 16 3 13
Cusp forms 4 1 3
Eisenstein series 12 2 10

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.1.h.a 320.h 20.d $1$ $0.160$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)