Properties

Label 320.2.f
Level $320$
Weight $2$
Character orbit 320.f
Rep. character $\chi_{320}(289,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

Trace form

\( 12q + 12q^{9} + O(q^{10}) \) \( 12q + 12q^{9} + 12q^{25} - 24q^{41} - 12q^{49} - 24q^{65} - 36q^{81} - 72q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
320.2.f.a \(4\) \(2.555\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots\)
320.2.f.b \(8\) \(2.555\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)