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Properties

Label 320.2.be
Level $320$
Weight $2$
Character orbit 320.be
Rep. character $\chi_{320}(21,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $256$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.be (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 400 256 144
Cusp forms 368 256 112
Eisenstein series 32 0 32

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 16 q^{22} - 80 q^{24} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{42} - 16 q^{44} - 32 q^{51} + 96 q^{52} + 64 q^{54} + 16 q^{56} + 144 q^{58} - 64 q^{59} + 96 q^{62} - 160 q^{63} + 96 q^{64} + 96 q^{66} - 160 q^{67} + 96 q^{68} - 64 q^{71} + 144 q^{72} + 16 q^{74} + 64 q^{76} + 48 q^{78} - 32 q^{79} - 64 q^{80} - 112 q^{84} - 208 q^{86} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96} - 272 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.2.be.a 320.be 64.i $256$ $2.555$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

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

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