Properties

Label 32.6.b
Level $32$
Weight $6$
Character orbit 32.b
Rep. character $\chi_{32}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(32, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 16 4 12
Eisenstein series 8 2 6

Trace form

\( 4 q - 96 q^{7} - 164 q^{9} + O(q^{10}) \) \( 4 q - 96 q^{7} - 164 q^{9} + 416 q^{15} + 200 q^{17} - 2336 q^{23} + 1556 q^{25} + 12928 q^{31} - 2352 q^{33} - 35104 q^{39} - 4568 q^{41} + 54720 q^{47} + 9828 q^{49} - 85472 q^{55} - 2032 q^{57} + 153440 q^{63} - 19520 q^{65} - 206688 q^{71} + 39976 q^{73} + 247872 q^{79} + 29684 q^{81} - 307872 q^{87} - 84632 q^{89} + 259744 q^{95} - 99576 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.6.b.a 32.b 8.b $4$ $5.132$ 4.0.218489.1 None \(0\) \(0\) \(0\) \(-96\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-24-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)