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Properties

Label 32.17.c
Level $32$
Weight $17$
Character orbit 32.c
Rep. character $\chi_{32}(31,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $68$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 32.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(68\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(32, [\chi])\).

Total New Old
Modular forms 68 16 52
Cusp forms 60 16 44
Eisenstein series 8 0 8

Trace form

\( 16 q - 354144 q^{5} - 275149040 q^{9} + O(q^{10}) \) \( 16 q - 354144 q^{5} - 275149040 q^{9} - 1853793632 q^{13} + 2869077792 q^{17} + 104597086720 q^{21} + 293211351600 q^{25} - 123085827936 q^{29} - 4204914725632 q^{33} - 642994992480 q^{37} + 11147491958304 q^{41} + 43380373401248 q^{45} - 126173640481776 q^{49} - 105959375753568 q^{53} + 410082678415104 q^{57} + 710697629293216 q^{61} - 910355863258560 q^{65} - 2697059112192512 q^{69} + 837568600702752 q^{73} + 2118009057234432 q^{77} + 4296817758308624 q^{81} + 4866664618702656 q^{85} - 5603031404382432 q^{89} - 19566037058828288 q^{93} + 1456754366180128 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.17.c.a 32.c 4.b $8$ $51.944$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 32.17.c.a \(0\) \(0\) \(-1121456\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-140182-\beta _{2})q^{5}+(-221\beta _{1}+\cdots)q^{7}+\cdots\)
32.17.c.b 32.c 4.b $8$ $51.944$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 32.17.c.b \(0\) \(0\) \(767312\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(95914-\beta _{3})q^{5}+(68\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{17}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{17}^{\mathrm{old}}(32, [\chi]) \simeq \) \(S_{17}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)