Properties

Label 32.8.b
Level $32$
Weight $8$
Character orbit 32.b
Rep. character $\chi_{32}(17,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(32, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 6 18
Eisenstein series 8 2 6

Trace form

\( 6 q + 688 q^{7} - 2918 q^{9} + O(q^{10}) \) \( 6 q + 688 q^{7} - 2918 q^{9} - 17872 q^{15} + 1452 q^{17} + 1296 q^{23} - 39314 q^{25} + 89280 q^{31} + 53880 q^{33} + 328208 q^{39} + 521244 q^{41} - 1566432 q^{47} - 511050 q^{49} + 3270256 q^{55} - 1889896 q^{57} - 5776816 q^{63} + 1416480 q^{65} + 7597104 q^{71} + 2089564 q^{73} - 16015904 q^{79} - 723058 q^{81} + 37453776 q^{87} + 2169084 q^{89} - 48537936 q^{95} - 1088308 q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.8.b.a 32.b 8.b $6$ $9.996$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(688\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(115+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)