Properties

Label 192.3.e
Level $192$
Weight $3$
Character orbit 192.e
Rep. character $\chi_{192}(65,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $6$
Sturm bound $96$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14 q - 2 q^{9} + O(q^{10}) \) \( 14 q - 2 q^{9} - 12 q^{13} + 20 q^{21} - 34 q^{25} + 84 q^{37} + 10 q^{49} + 60 q^{57} - 76 q^{61} - 256 q^{69} - 4 q^{73} - 146 q^{81} - 256 q^{85} + 308 q^{93} + 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.3.e.a 192.e 3.b $1$ $5.232$ \(\Q\) \(\Q(\sqrt{-3}) \) 12.3.c.a \(0\) \(-3\) \(0\) \(-2\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
192.3.e.b 192.e 3.b $1$ $5.232$ \(\Q\) \(\Q(\sqrt{-3}) \) 12.3.c.a \(0\) \(3\) \(0\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\)
192.3.e.c 192.e 3.b $2$ $5.232$ \(\Q(\sqrt{-2}) \) None 24.3.e.a \(0\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots\)
192.3.e.d 192.e 3.b $2$ $5.232$ \(\Q(\sqrt{-2}) \) None 24.3.e.a \(0\) \(2\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots\)
192.3.e.e 192.e 3.b $4$ $5.232$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 96.3.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
192.3.e.f 192.e 3.b $4$ $5.232$ \(\Q(\sqrt{-2}, \sqrt{7})\) None 96.3.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)