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Properties

Label 640.2.x
Level $640$
Weight $2$
Character orbit 640.x
Rep. character $\chi_{640}(81,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(640, [\chi])\).

Total New Old
Modular forms 416 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(640, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
640.2.x.a 640.x 32.g $64$ $5.110$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)