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Properties

Label 32.3.d
Level $32$
Weight $3$
Character orbit 32.d
Rep. character $\chi_{32}(15,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(32, [\chi])\).

Total New Old
Modular forms 12 3 9
Cusp forms 4 1 3
Eisenstein series 8 2 6

Trace form

\( q + 2 q^{3} - 5 q^{9} + O(q^{10}) \) \( q + 2 q^{3} - 5 q^{9} - 14 q^{11} + 2 q^{17} + 34 q^{19} + 25 q^{25} - 28 q^{27} - 28 q^{33} - 46 q^{41} - 14 q^{43} + 49 q^{49} + 4 q^{51} + 68 q^{57} + 82 q^{59} - 62 q^{67} - 142 q^{73} + 50 q^{75} - 11 q^{81} - 158 q^{83} + 146 q^{89} - 94 q^{97} + 70 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.3.d.a 32.d 8.d $1$ $0.872$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{3}-5q^{9}-14q^{11}+2q^{17}+34q^{19}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)