Properties

Label 32.18.b
Level $32$
Weight $18$
Character orbit 32.b
Rep. character $\chi_{32}(17,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 18 \)
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: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(32, [\chi])\).

Total New Old
Modular forms 72 18 54
Cusp forms 64 16 48
Eisenstein series 8 2 6

Trace form

\( 16 q - 11529600 q^{7} - 602654096 q^{9} + O(q^{10}) \) \( 16 q - 11529600 q^{7} - 602654096 q^{9} + 9993282176 q^{15} - 7489125600 q^{17} - 746845345920 q^{23} - 1809682431664 q^{25} + 318979758592 q^{31} + 5633526177600 q^{33} + 18457706051456 q^{39} + 7482251536032 q^{41} + 376698804821760 q^{47} + 127691292101520 q^{49} - 2209036687713152 q^{55} - 190521298294720 q^{57} + 8131096607338880 q^{63} + 2385987975356160 q^{65} - 9025926285576576 q^{71} + 11332002046118560 q^{73} + 45299671392008448 q^{79} + 20101901999290832 q^{81} - 25965768920837760 q^{87} - 69879174608766048 q^{89} - 93790444358203776 q^{95} + 95593398602180640 q^{97} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.18.b.a 32.b 8.b $16$ $58.631$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-11529600\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(4\beta _{1}-\beta _{9})q^{5}+(-720600+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{18}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)