Properties

Label 320.3.e
Level $320$
Weight $3$
Character orbit 320.e
Rep. character $\chi_{320}(159,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(320, [\chi])\).

Total New Old
Modular forms 108 24 84
Cusp forms 84 24 60
Eisenstein series 24 0 24

Trace form

\( 24q - 72q^{9} + O(q^{10}) \) \( 24q - 72q^{9} - 72q^{25} - 240q^{41} + 168q^{49} + 144q^{65} + 120q^{81} + 48q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
320.3.e.a \(8\) \(8.719\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots\)
320.3.e.b \(16\) \(8.719\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(-6-\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)