Properties

Label 16.9.c
Level $16$
Weight $9$
Character orbit 16.c
Rep. character $\chi_{16}(15,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $18$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 16.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(16, [\chi])\).

Total New Old
Modular forms 19 4 15
Cusp forms 13 4 9
Eisenstein series 6 0 6

Trace form

\( 4 q - 504 q^{5} - 14460 q^{9} + O(q^{10}) \) \( 4 q - 504 q^{5} - 14460 q^{9} - 17144 q^{13} - 16632 q^{17} + 634368 q^{21} - 909172 q^{25} + 1794312 q^{29} - 6084864 q^{33} + 6684680 q^{37} - 8799480 q^{41} + 17157384 q^{45} - 11755772 q^{49} + 24716808 q^{53} - 26616576 q^{57} - 30823672 q^{61} + 38139408 q^{65} - 42591744 q^{69} + 38504968 q^{73} - 54738432 q^{77} + 183934980 q^{81} - 81659376 q^{85} + 139985928 q^{89} - 362981376 q^{93} + 148649224 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.9.c.a 16.c 4.b $2$ $6.518$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(-1020\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots\)
16.9.c.b 16.c 4.b $2$ $6.518$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(516\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)