Properties

Label 320.2.d
Level $320$
Weight $2$
Character orbit 320.d
Rep. character $\chi_{320}(161,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

Trace form

\( 8 q - 8 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{9} - 8 q^{25} - 48 q^{33} + 48 q^{41} + 40 q^{49} + 16 q^{57} - 32 q^{73} + 8 q^{81} - 48 q^{89} + 32 q^{97} + O(q^{100}) \)

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.d.a \(4\) \(2.555\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-12\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.d.b \(4\) \(2.555\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(12\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)