↑

Properties

Label 16.15.c
Level $16$
Weight $15$
Character orbit 16.c
Rep. character $\chi_{16}(15,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $30$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 16.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(16, [\chi])\).

Total New Old
Modular forms 31 7 24
Cusp forms 25 7 18
Eisenstein series 6 0 6

Trace form

\( 7 q - 24186 q^{5} - 21296049 q^{9} + O(q^{10}) \) \( 7 q - 24186 q^{5} - 21296049 q^{9} + 139092886 q^{13} + 710175342 q^{17} - 1415952384 q^{21} + 11435621981 q^{25} + 63435031734 q^{29} - 2039491584 q^{33} - 263726136250 q^{37} + 189781331742 q^{41} + 320749335126 q^{45} - 1861714652105 q^{49} - 3740081879322 q^{53} + 8528108338176 q^{57} - 740171459722 q^{61} + 12045273853020 q^{65} - 6670732879872 q^{69} + 10508042495518 q^{73} - 89617501145088 q^{77} + 166950156099159 q^{81} - 169851174341940 q^{85} + 110507925483582 q^{89} - 360163971588096 q^{93} + 373205288690446 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.15.c.a 16.c 4.b $1$ $19.893$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-152886\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-152886q^{5}+3^{14}q^{9}-46322630q^{13}+\cdots\)
16.15.c.b 16.c 4.b $2$ $19.893$ \(\Q(\sqrt{-3395}) \) None \(0\) \(0\) \(215700\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+107850q^{5}+522\beta q^{7}-3039111q^{9}+\cdots\)
16.15.c.c 16.c 4.b $4$ $19.893$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-87000\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-21750+\beta _{3})q^{5}+(245\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{15}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)