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Properties

Label 512.2.k
Level $512$
Weight $2$
Character orbit 512.k
Rep. character $\chi_{512}(17,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $240$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.k (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(512, [\chi])\).

Total New Old
Modular forms 1088 272 816
Cusp forms 960 240 720
Eisenstein series 128 32 96

Trace form

\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(512, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
512.2.k.a 512.k 128.k $240$ $4.088$ None 128.2.k.a \(0\) \(16\) \(-16\) \(16\) $\mathrm{SU}(2)[C_{32}]$

Decomposition of \(S_{2}^{\mathrm{old}}(512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)